Publications of Steven Dougherty

Books 

1. Algebraic Coding Theory over Finite Commutative Rings, Springer-Verlag, ISBN-13: 978-3319598055.  You can buy it here.

2. Combinatorics and Finite Geometry, Springer-Verlag, ISBN: 978-3-030-56394-3. You can buy it here. Corrections can be found here.

  Papers 

3. Nets and their codes, Designs, Codes and Cryptography, 3, 315-331, 1993.

4. A Coding-Theoretic Solution to the 36 Officer Problem, Designs, Codes and Cryptography, 4, 123-128, 1994.

5. Shadow Codes and their Weight Enumerators, IEEE Transactions on Information Theory, Volume 41, Number 3, May 1995.

6. Extremal Binary Self-dual Codes, IEEE Transactions on Information Theory, 2036-2047, November 1997, with M. Harada and T.A. Gulliver.

7. Planes, Nets and Codes, Mathematical Journal of Okayama University Vol 38, December 1996.

8. Type II Codes Over F_2 + u F_2, IEEE-IT, vol 45. No. 1, January 1999, with M. Harada, P. Gaborit, and P. Sole.

9. Optimal Ternary Formally Self-dual Codes, Discrete Mathematics 196, 1999, 117-135, with T.A. Gulliver an M. Harada.

10. Type II Codes, Even Unimodular Lattices, and Invariant Rings, IEEE-IT, Volume 45, Number 4, 1999, 1194-1205, with E. Bannai, M. Harada, and M. Oura.

11. Self-Dual Codes over Rings and the Chinese Remainder Theorem, Hokkaido Math Journal, Volume 28, 1999, 253-283, with M. Harada and P. Sole.

12. Type II Self-Dual Codes over Finite Rings and Even Unimodular Lattices, Journal of Algebraic Combinatorics, Volume 9, Issue 3, 1999, p. 233-250, with T.A. Gulliver and M. Harada.

13. Shadow Optimal Self-Dual Codes, Kyushu Journal of Mathematics, Vol 53, No. 2., 1999, p. 223-237, with M. Harada.

14. Type IV Self-Dual Codes over Rings, IEEE-IT, Vol 45, No. 7, November 1999, p. 2345-2360, with P. Gaborit, M. Harada, A. Munemasa, and P. Sole.

15. MDR Codes over Z_k, IEEE-IT, Vol 46, No. 1, January 2000, p. 265-269, with Keisuke Shiromoto.

16. New Extremal Codes of Length 68, IEEE-IT, Vol 46, No. 6, 2133-2136, September 1999, with M. Harada.

17. Self-Dual Codes and Finite Projective Planes , Mathematical Journal of Okayama University, Vol. 40, 1998,2000.

18. Shadow Lattice and Shadow Codes, Discrete Math, Vol. 219 (2000), 49-64, with M. Harada and P. Sole.

19. Optimal Formally Self-Dual Codes over F_5 and F_7, AAECC, 10, No. 3, 227-236,2000, with M. Harada and T.A. Gulliver.

20. Maximum Distance Codes over Rings of Order 4, IEEE-IT, Vol 47, No 1, January 2001, with Keisuke Shiromoto.

21. Note on g-fold joint weight enumerators of self-dual codes over Z_k, AAECC, Vol 11, 437-445, 2001. with Masaaki Harada and Manabu Oura.

22. Higher Weights and Binary Self-Dual Codes, Electronic Notes in Applied Mathematics, April, 2001, with T. Aaron Gulliver.

23. Shadow Codes over Z_4, Finite Fields and their Applications, Vol. 7, No. 4, (2001), 507-529, with M. Harada and P. Sole.

24. MacWilliams Duality and the Rosenbloom-Tsfasman Metric, Moscow Mathematical Journal, Vol. 2, Number 1, 2002, 83-99, with M.M. Skriganov.

25. Shadow Constructions of Unimodular Lattices and Self-Dual Codes, AMC, Ed. T. Sunada, BW Sy, Y. Lo. World Sicentific, 2002, 139-152, with P. Sole.

26. Maximum Distance Separable Codes in a Non-hamming Metric over Arbitrary Alphabets , Journal of Algebraic Combinatorics, Volume 16, 71-81, 2002, with M.M. Skriganov.

27. 2-modular Lattices from Ternary Codes, Journal de Theorie des Nombres de Bordeaux, Volume 14, 2002, 73-85, with R. Chapman, P. Sole, and P. Gaborit.

28. Generalized Shadows of Codes over Rings, Hokkaido Mathematical Journal, Vol XXXII, No 1, February 2003, 101-116.

29. Cubic Self-Dual Binary Codes, IEEE Transactions on Information Theory, Volume 49, Number 9, September 2003, 2253-2259, with A. Bonnecaze, L. Nochefranca, Anne Desideri Bracco and P. Sole.

30. Splitting the Shadow, Discrete Mathematics 270, 2003, 43-60, with A. Bonnecaze, Y. Choie and P. Sole.

31. Higher Weights and Graded Rings for Binary Self-Dual Codes, Applied Discrete Mathematics, Volume 128, Issue 1, 121-143, with T. Aaron Gulliver and Manabu Oura.

32. Maximum Distance Codes in Mat_{n,s}(Z_k) with a Non-Hamming Metric and Uniform Distributions, Designs, Codes and Cryptography, Volume 33, 1, 45-61, 2004, with Keisuke Shiromoto.

33. Tic-Tac-Toe on a Finte Plane, Math Magazine, 260-274, October 2004, with Maureen Carroll. (Awarded Hasse Prize 2005).

34. Codes over Sigma_{2m} and Jacobi Forms over the Quaternions, Appl. Algebra. Engr. Com. Comput. 15, 2004 No. 2, 129-147, with YoungJu Choie.

35. Generalized Weights for Codes over Finite Rings, AJC, 31, 2005, 231-248, with M. Gupta and K. Shiromoto.

36. A New Construction of Self-Dual Codes from Projective Planes, AJC, 31, 2005, 337-348.

37. Codes over Rings, Complex Lattices, and Hermitian Modular Forms, European Journal of Combinatorics, 26, 2005, No. 2, 145-165, with YoungJu Choie.

38. Complete Joint Weight Enumerators and Self-Dual Codes, IEEE-IT, 49, No. 5, 2003, 1275-1282, with Young Ju Choie and Haesuk Kim.

39. Lifted Codes and their Weight Enumerators, Discrete Mathematics, 305, Vol 1-3, 2005, 123-135, with Young Ho Park and Sun Young Kim.

40. Higher Weights for Ternary and Quaternary Self-Dual Codes, Designs, Codes and Cryptography, 38, 97-112, 2006, with T. Aaron Gulliver and Manabu Oura.

41. Codes over the p-adic integers, Designs, Codes and Cryptography, April 2006, 65-80, with Young Ho Park.

42. Cyclic codes over Z_4 of even length, Designs, Codes and Cryptography, May 2006, 127-153, with San Ling.

43. Double Circulant Codes from Two Class Association Schemes, with Jon-Lark Kim and P. Sole, AMC, Volume 1, Number 1.

44. Self-dual codes over Z_8 and Z_9 , Designs, Codes and Cryptography, 41, 235-249, 2006, with T. Aaron Gulliver and John Wang.

45. On Modular Cyclic Codes, Finite Fields and their Applications Volume 13, Number 1, 31-57, 2007, with Young Ho Park.

46. Optimal Linear Codes over Z_m, Journal of the Korean Mathematical Society, 44, 2007, No.5, 1139-1162, with T. Aaron Gulliver, Young Ho Park and John Wang.

47. Symmetric Designs and Self-Dual Codes over Rings, Ars Combinatoria, Vol. 85, 2007, with Aaron Gulliver and Reshma Ramadurai.

48. Latin k-hypercubes, AJC, Volume 40, February 2008, with T. Szczepanski.

49. Higher Weights of Codes from Projective Planes and Biplanes, Mathematical Journal of Okayama University, Vol. 49, 2007, with Reshma Ramadurai.

50. The nature of coding theory, News Letter of the Korean Mathematical Society, July 2007, 26-31. (appears in Korean)

51. MDS codes over finite principal ideal rings, Designs, Codes and Cryptography, Volume 50, 77-92, 2009, with Jon-Lark Kim and Hamid Kulosman.

52. Independence of vectors in codes over rings, Designs, Codes and Cryptography, 55-68, 2009, with Hongwei Liu.

53. Type II codes over finite rings, Science in China, Volume 53, Number 1, 203-212, with Hongwei Liu.

54. Self-Dual codes over Frobenius Rings, with J.L. Kim, H. Kulosman and Hongwei Liu, Finite Fields and their Applications, Volume 16, January 2010, 14-26.

55. Constructions of self-dual codes over chain rings, with Hongwei Liu and Jon-Lark Kim, International Journal of Information and Coding Theory, Volume 1, Number 2, 171-190.

56. Lifted Codes over Finite Chain Rings, with Hongwei Liu and Young Ho Park, Mathematical Journal of Okayama University Volume 53, January 2010, 39-53.

57. Cyclic Codes over Formal Power Series, with Hongwei Liu, Acta Mathematica Scientia 2010, 31 B (1): 331-343.

58. Higher Weights and Generalized MDS codes, with Sunghyu Han, Korean Mathematical Society, Volume 47, Number 6, 2010, 1167-1182.

59. Higher Weights for Codes over Rings, Applicable Algebra in Engineering, Communication and Computing, with Sunghyu Han and Hongwei Liu.

60. Maximum Distance Separable codes over Z_4 and Z_2 X Z_4, Designs, Codes and Cryptography, Volume 61, Issue 1, 2011, 31-40, with M. Bilal, J. Borges, and C. Fernandez-Cordoba.

61. Codes over R_k, Gray maps and their Binary Images, with Bahattin Yildiz and Suat Karadeniz,  Finite Fields and their Applications, Volume 17, Number 3, 205-219, 2011.

62. Codes over Z_{2^k}, Gray maps and Self-Dual Codes, with Cristina Fernandez-Cordoba, Advances in Mathematics of Communication, Volume 5, Number 4, November 2011.

63. Cyclic Codes over R_k, with Bahattin Yildiz and Suat Karadeniz,  Designs, Codes and Cryptography, Volume 63, Number 1.

64. Self-Dual codes over Z2 x Z4 , with J. Borges and Cristina Fernandez-Cordoba, AMC, Volume 6, Number 4, 287-303, 2012.

65. Amidakuji and Games, with Jennifer Franko Vasquez,  Journal of Recreational Mathematics, Volume 37 (1), 46-56, 2008.

66. Z_2Z_4-Additive Formally Self-Dual Codes, with C. Fernandez-Cordoba,  Designs, Codes and Cryptography, Dec. 2012.

67. Jacobi Forms and Hilbert-Siegel Modular Forms over Totally Real Fields and Self-Dual Codes over Polynomial Rings Z_2m[x]/g(x), with YoungJu Choie and Hongwei Liu,  Ars Combinatoria, 107, 2012, 141-160.

68. Self-dual Codes over R_k and Binary Self-Dual Codes, with Bahattin Yildiz and Suat Karadeniz,  European Journal of Pure and Applied Mathematics, Volume 6, Number 1, Feb. 2013.

69. Counting Codes over Rings, Designs, Codes and Cryptography,  2013,   with Esengul Salturk.

70. Indivisibles, infinitesimals and a tale of seventeenth century mathematics, Mathematics Magazine, 86 (2013, no. 4, 239-254, with M.T. Carroll and Dave Perkins.

71. Constructing Formally Self-Dual Codes over R_k, with Bahattin Yildiz and Suat Karadeniz,  Discrete Applied Mathematics, December 2013. 

72. Linear Codes, Hermitian Lattices, and Finite Rings, with Jon-Lark Kim and Yoonjin Lee,  Designs, Codes and Cryptography, 2014.

73. Codes over an Infinite Family of Rings with a Gray Map, with Yasemin Cengellenmis and Abdullah Dertli,  Designs, Codes and Cryptography, Volume 72, Number 3, 2014, 559-580.

74. Foundations of Algebraic Coding Theory,  Contemporary Mathematics, Volume 634,  2015, 101 - 136.

75. Counting Additive Z2Z4 codes, with Esengul Salturk,  Contemporary Mathematics, Volume 634, 2015, 137 - 147.

76. Open Problems in Coding Theory, with Jon-Lark Kim and P. Sole,  Contemporary Mathematics, Volume 634, 2015, 79 - 99.

77.  Self-dual codes from 3-class association schemes, with M. Bilal, J. Borges and C. Fernandez-Cordoba, Appl. Algebra Engrg. Comm. Comput. 26 (2015), No. 3, 227 -250.

78. One weight Z2Z4 additive codes,  Applicable Algebra in Engineering, Communication and Computing, Volume 27, No. 2, DOI 10.1007/s00200-015-0273-4  with Hongwei Liu and Long Yu. 

79. Self-dual codes over non-commutative Frobenius rings, with André Leroy,  Applicable Algebra in Engineering, Communication and Computing, 27 (3), 185-203, 2016,  DOI 10.1007/s00200-015-0277-0. 

80. Kernels and Ranks of Cyclic and Negacyclic Quaternary Codes, with Cristina Fernandez-Cordoba.,  Designs, Codes and Cryptography, Volume 81, Number 2, 347 -            364, 2016, (DOI) 10.1007/s10623-015-0163-6.

81. Ranks and Kernels of Codes from Generalized Hadamard Matrices, with Josep Rifa and Merce Villanueva, IEEE transactions on Information Theory, February 2016, Volume 62, Issue 2, pages 1-8, Print ISSN 0018-9448, Online ISSN 1557-9654, DOI 10.1109/TIT.2015.2509061.

82. Theta cyclic codes over A_k, with Aleams Barra, Irwansyah, A. Muclis, I. Alamsyah, P. Sole and Olfa Yemen, International Journal of Computer Mathematics, Computer Systems Theory, DOI:10.1080/23799927.2016.1146800

83.  Constructions of Self-Dual Codes and Formally Self-Dual Codes over Rings,  AAECC, Volume 27, Number 5, 435 - 449,  DOI 10.1007/s00s00-016-0288-5, 2016, with  Abidin Kaya and Esengul Salturk.

84. Quasi-Cyclic Codes as Cyclic Codes over a Family of  Local Rings, Finite Fields and Their Applications (2016), 138-149,  with Cristina, Fernandez-Cordoba and Roger Ten-Valls.

85. On codes over Z_{p^e} with extended Lee weight,  Filomat, Volume 30, Number 2 (2016). with Zeynep Ozger and Bahattin Yildz.

86. Codes over local rings of order 16 and binary codes, Advances in Mathematics of Communication, Vol. 10, no. 2 May 2016, 379 - 391, with Esengul  Salturk and Steve Szabo. 

87. Codes Over a Family of Local Frobenius Rings, Gray Maps and Self-Dual Codes,   Discrete Applied Mathematics,  DOI: 10.1016/j.dam.2016.09.025, with Esengul Salturk.

88. On the duality and the direction of polycyclic codes,   Advances in Mathematics of Communication, Vol 10, No. 4, November 2016, with Adel Alahamdi, Andre Leroy and Patrick Sole.

89.  Cyclic Codes over Local Frobenius Rings of Order 16, Advances in Mathematics of Communication, Volume 11, No. 1, 2017, 99 - 114, with Abidin Kaya and Esengul Salturk.

90. Signed Permutations and the Braid Group, with Michael Allocca and Jennifer Vasquez, Rocky Mountain Mathematics Journal, 47, 2017, n0 2., 391-402. 

91. Codes and the Steenrod Algebra, J. Algebra Comb. Discrete Struct. Appl. 4 (2017), no. 2, 141-154, with Tane Vergili.

92. The combinatorics of LCD codes: Linear Programming bound and orthogonal matrices, with J.L. Kim. B. Ozkaya, L. Sok, and P. Sole, International Journal of Information and Coding Theory, Volume 4 (2017), no. 2-3, 116- 128. 

93. Group Rings, G-Codes and Constructions 0f Self-Dual and Formally Self-Dual Codes, Designs, Codes and Cryptography, Designs, Codes and Cryptography, 86(9), 2115-2138, 10.1007/s10623-017-0440-7, with J. Gildea, R. Taylor and A.  Tylshchak. 

94. Additive Self-Dual Codes over Fields of Even Order,  Bulletin of the Korean Mathematical Society,  Vol. 55, No. 2, 341-357, 2018, with Jon-Lark Kim and Nari Lee.

95. Binary Images of Z2Z4-Additive Cyclic Codes, IEEE-IT, April, 2019, Volume 65, Number 4, 2119-2127,  Print ISSN: 0018-9448. Online ISSN: 1557-9654Digital Object Identifier: 10.1109/TIT.2018.2870891 with J.Borges, C. Fernandez, and R. Ten.

96. Bordered Constructions of Self-Dual Codes from Group Rings and New Extremal Binary Self-Dual Codes, with J. Gildea A. Korban, A. Kaya, A. Tylyshchak and B. Yildiz,  Finite Fields Appl. 57 (2019), 108–127.

97. On codes over local Frobenius rings: Generator matrices, Generating characters and MacWilliams Identities, with Esengul Salturk and Steve Szabo, AAECC, https://doi.org/10.1007/s00200-019-00384-0.

98. Construction and enumeration for self-dual cyclic codes over Z4 of oddly even length,  Designs, Codes and Cryptography, Designs, Codes and Cryptography, 87(10), 2419-2446, DOI 10.1007/s10623-019-00629-6, with Y. Cao, Yuan Cao, Yonglin Cao, and S. Ling. 

99. Constacyclic Codes Over Local Rings of Order 16, with Esengul Salturk, Contemporary Mathematics, Volume 727, 2019 https://doi.org/10.1090/conm/727/14627.

100. Generating Characters of Non-commutative Rings, with Arda Kol and Andre Leroy, Contemporary Mathematics, Volume 727, 2019 https://doi.org/10.1090/conm/727/14626.  

101. New Self-Dual and Formally Self-Dual Codes from Group Ring Constructions,  Advances in Mathematics of Communications doi:10.3934/amc.2020002, Volume 14, No. 1, 2020, 11–22, with J. Gildea, A. Kaya and B. Yildiz.

102. Skew Cyclic and Skew Constacyclic Codes over the local Frobenius Non-Chain Rings of Order 16, with N. Aydin, Y. Cengellenmis, A. Detli and E. Salturk,  AMC, 2020, 14(1): 53-67 doi: 10.3934/amc.2020005. 

103. Composite Constructions of Self-Dual Codes from Group Rings and New Extremal Self-Dual Binary Codes of length 68, with Joe Gildea, Abidin Kaya and Adrian Korban,  AMC, doi: 10.3934/amc.2020037.  

104. On Z_2\Z_4-additive complementary dual codes and related LCD codes, Finite Fields and Their Applications, https://doi.org/10.1016/j.ffa.2019.101622, with N. Benbelkacem, J. Borges and Cristina Fernandez-Cordoba.

105. $G$-codes over Formal Power Series Rings and Finite Chain Rings, Journal of Algebra, Combinatorics, Discrete Structures and Applications, Volume 7, Issue 1, 55 - 71,  with Joe Gildea and Adrian Korban.

106. Quadruple Bordered Constructions of Self-Dual Codes from Group Rings over Frobenius Rings, Cryptography and Communications, 12(1), 127-146, DOI 10.1007/s12095-019-00380-8 with Joe Gildea and Abidin Kaya.

107. Algebraic Structure of Additive Conjucyclic Codes Over F_4, Finite Fields and their Applications, https://doi.org/10.1016/j.ffa.2020.101678, with Tahuer Abualrub and Yonglin Cao.

108. Quaternary Group Rings: Ranks, Kernels and Self-Dual Codes, Advances of Mathematics of Communication, Volume 14, May 2020, Issue 2, with C. Fernandez-Cordoba, R. Ten and B. Yildiz.

109. Double Quadratic Residue Codes and Self-Dual Double Cyclic Codes, Applicable Algebra in Engineering, Communication and Computing,  1-25, DOI: 10.1007/s00200-020-00437-9 with Taher Abualrub and Arezoo Soufi Karbaski.

110. New Extremal Binary Self-Dual Binary Codes of Length 68 via Composite Construction, F_2+uF_2 Lifts, Extensions and Neighbors, Int. J. Information and Coding Theory, Vol. 5, Nos. 3/4, 2020, with Joe Gildea, Abidin Kaya and Adrian Korban.

111. Self-Dual Codes over a Family of Local Rings, Applicable Algebra in Engineering, Communication and Computing, 32 (3), 265-281.  https://doi.org/10.1007/s00200-020-00466-4with C. Fernandez-Cordoba and Roger Ten.

112. Linear Transformation Codes: Codes with a Compact Description and Transpolizer Codes, Int. J. Information and Coding Theory, Vol. 5, Nos. 3/4, 2020, with Bahattin Yildiz.

113. Self-Dual Additive Codes,  with A. Korban and S. Sahinkaya, Applicable Algebra in Engineering, Communication and Computing, 1- 18, DOI 10.1007/s00200-020-00473-5.

114. Extending an Established Isomorphism between Group Rings and a Subring of n by n Matrices, International Journal of Algebra and Computation, https://doi.org/10.1142/S0218196721500223 with Adrian Korban and J. Gildea. 

115. Group Matrix Ring Codes and Constructions of Self-Dual Codes, with A. Korban, S. Sahinkaya and Deniz Ustun,  Applicable Algebra in Engineering, Communication and Computing, 10.1007/s00200-021-00504-9, Volume 4, Issue 2.    

116. G-Codes Self-Dual G-Codes and Reversible Codes over B_{j,k}, Cryptography and Communications, 10.1007/s12095-021-00487-x, May 3, 2021,  with Adrian Korban and Serap  Sahinkaya.

117. Additive Skew G Codes, Applicable Algebra in Engineering, Communication and Computing https://doi.org/10.1007/s00200-021-00515-6, Applicable Algebra in Engineering, Communications, and Computing, Volume 34, Issue 3,  with A. Korban, S. Sahinkaya and Deniz Ustun.

118. Composite Matrices from Group Rings, Composite G-Codes and Constructions of Self-Dual Codes, with A. Kaya, A. Korban and J. Gildea, Designs, Codes and Cryptography, 2021.

119. Rank and kernel of F_p-Additive Generalised Hadamard Codes, with Josep Rifa and Merce Villanueva, IEEE Transactions on Information Theory, Print ISSN: 0018-9448, Online ISSN: 1557-9654,Digital Object Identifier: 10.1109/TIT.2021.3100433.

120. Orthogonality from Group Characters,  Involve,  Volume 14, No. 14,  2021, with Sara Myers. 

121. Reversible  G codes over the ring F_jk with application to DNA Codes, Advances in Mathematics of Communication.  2021, Doi 10.3934/amc.2021056 with Y. Cengellemis, A. Dertli, A. Korban and S. Sahinkaya.

122. Additive and Linear Conjucyclic Codes over F_4, Advances in Mathematics of Communications, Volume 16, no. 1, February 2022, with Taher Abualrub. 

123. Additive Complementary Dual Codes from Group Characters, with S. Sahinkaya, IEEE Transactions on Information Theory, Print ISSN: 0018-9448, Online ISSN: 1557-9654,  Digital Object Identifier: 10.1109/TIT.2022.3162181.

124. The Neighbor Graph of Binary Self-Dual Codes, Des. Codes, Cryptog. 90, (2022), no. 2, 409-425. 

125. Binary Self-Dual and LCD Codes from  Generator Matrices Constructed from Two Group Ring Elements by a Heuristic Search Scheme, with A. Korbin, S. Sahinkaya, and D. Ustun, Advances of Mathematics of Communication,   DOI: 10.3934/amc2022036. 

126. DNA Codes from Skew Dihedral Group Rings,  with A. Korbin, S. Sahinkaya, and D. Ustun, AMC, Volume 18, Issue 4: 1138-1154, 2024,  DOI  10.3934/amc2022076. 

127. On Cyclic and Negacyclic Codes with One-Dimensional Hulls and Their Applications, with S. Sahinkaya, AMC,  Volume 18, Issue 5, 1364-1378, 2024, DOI: 10.3934/amc/2022096, 2022. 

128. Construction of DNA Codes from Composite Matrices and a Bio-inpired Algorithm, with A. Korban, S. Sahinkaya and Deniz Ustun, to appear in IEEE-IT, IEEE Transactions on Information Theory, MARCH 2023, Volume: 69, Issue: 3, Page(s): 1588-1603, Print ISSN: 0018-9448, Online ISSN: 1557-9654, Digital Object Identifier: 10.1109/TIT.2022.3217518.

129. Dualities Over the Cross Product of the Cyclic Groups of Order $2$, with S. Sahinkaya.  Volume 18, Issue 5, 1531-1546, 2024. AMC DOI: 10.3934/amc2023005.

130. Dualities for Codes over Finite Abelian Groups, Advance in Mathematics of Communication,  Volume 18, Issue 6, 1827-1841, 2024, Doi: 10.3934/amc.2023023, 2023.

131.  Dihedral Codes with $1$-dimensional Hulls and $1$-Dimensional Linear Complementary Pairs of Dihedral Codes,  Applicable Algebra in Engineering, Communication, and Computing, Volume 34, Issue 4, July 2023, with S. Sahinkaya, and S. Ustun.

132. Segre's theorem on ovals in Desarguesian projective planes, with Patrick Browne and Padraig O Cathain, Bulletin of the Irish Mathematical Society,  Volume 91,  37-47, (2023).  

133. The Number of Codes over Rings of Order $4$ Containing a  Hull of  Given Type, with Esengul Salturk, Advances in Mathematics of Communication Volume 19, Issue 1, 11-35, 2025, Doi: 10.3934/amc2023031, 2023. 

134. Codes over a ring of order 32 with Two Gray Maps, with J. Gildea, A. Korban, and A. Roberts, Finite Fields and their Applications, Volume 95, March 2024.

135. Distances in Graphs of Permutations, with Mia Gianello, Rocky Mountain Journal. Volume 54, No.2, 451-462, 2024.  

136. On Additive Codes with One Rank Hulls, with S. Sahinkaya, and D. Ustun, Applicable Algebra in Engineering, Communication and Computing, DOI 10.1007/s00s00-024-00663-5. 

137. The Neighbor Graph of Binary Self-Orthogonal Codes, with E. Salturk,  Advances in Mathematics of Communication,Volume 19, Issue 3, 963-979, 2025, Doi: 10.3934/amc2024035, 2024. 

138. Skew G codes,   with S. Sahinkaya and B. Yildiz. Journal of Algebra and its Applications, Volume 22, Number 02, 2350056, 2023, https://doi.org/10.1142/S0219498823500561. 

139. Foundations of Additive Codes over Finite Fields,  with D. K. Bhunia, C. Fernandez-Cordoba, M. Villanueva,  Finite Fields and their Applications, Volume 104, June 2025, 102592. 

140. On $Z_pZ_{p^2}...Z_{P^s} $-Additive Codes: Linearity, Duality and $(G_1,G_2,\dots,G_s)$-Codes, Advances in Mathematics of Communication, Doi: 10.3934/amc2025026 with Cristina Fernandez and Serap Sahinkaya.  

141. A New Characterization of Finite Commutative Frobenius Rings, to appear in Advances of Mathematics of Communication DOI: 10.3934/amc2025032, 2025.   

142. Coding Theory: The story of how an engineering problem evolved into a branch of pure mathematics, Irish Mathematical Society Bulletin, Volume 95, 3-22, Summer 2025, DOI: 10.33232/BIMS.0095.  

Book Chapters

143. Fun and Games with Squares and Planes, Resource for Teaching Discrete Mathematics, published by the MAA, 2009, with Maureen Carroll. 

144. Tic-tac-toe on affine planes,  The Mathematics of Various Entertaining Subjects, Princeton University Press, 2016, with Maureen Carroll.

145. Kings, Sages, Hats, and Codes, with Yusra Naqvi  in MOVES III.  

146. Bugs Braids, and Batching, with M. Allocca and J. Vasquez  in MOVES III.  

147. Codes over Rings, Chapter 6 in Concise Encyclopedia of Coding Theory, CRC Press, 2011.

  Refereed proceedings

148. Type II Self-Dual Codes over Finite Rings and Even Unimodular Lattices -- Proceedings IEEE-IT International Symposium on Information Theory, 1997 with T.A. Gulliver and Masaaki Harada, (presented by T.A. Gulliver).

149. Codes, Lattices and Modular Forms , Proceedings of the 2003 IEEE Information Theory Workshop, 259-262, with Young Ju Choie.

150. Optimal codes over Z2 X Z4, JMDA 2010, with M. Bilal, J. Borges, and C. Fernandez-Cordoba.

151. Additive Codes over Z2 x Z4, ITW 2010, Dublin, with J. Borges, and C. Fernandez-Cordoba.

152. Binary self-dual codes from 3-class association schemes, 3ICMCTA, with M. Bilal, J. Borges, and C. Fernandez-Cordoba. 

153. Formally self-dual codes and Gray maps, ACT2012, Pomorie, Bulgaria.

154. Cyclic codes over A_k,  Pomorie, Bulgaria, with Yasemine Cengellenmis.

155. Extensions of Z2Z4 Additive Self-Dual Codes Preserving Their Properties,   ISIT 2012, with M. Bilal, J. Borges, and C. Fernandez-Cordoba.

156. Constructions of Nonequivalent Fp-Additive Generalised Hadamard Codes, ISIT 2020, with Josep Rifà, and Mercè Villanueva.

To appear

157. 2^n Bordered Constructions of Self-Dual Codes from Group Rings, with Joe Gildea and Abidin Kaya, to appear in FFA.

158. Additive G-Codes over Fq and their Dualities, with Cristina Fernandez-Cordoba, to appear in FFA.

159. Quasi-Self-Dual Codes over the Non-Unital Ring $E$, with S. Sahinkaya, to appear in Contemporary Mathematics.

160. Group LCD and Group Reversible LCD Codes, with A. Korban, J. Gildea and A. Roberts, to appear in Finite Fields and their Applications.

161. Symplectically Self-Orthogonal Additive Codes and their Applications to Quantum Stabilizer Codes,  with N. Kashyap, T. Sidana, S. Sahinkaya, and D. Ustun, to appear in Contemporary Mathematics.

162. Codes constructed from Lie Algebras, with Joshua Carey, to appear in Contemporary Mathematics.

In submission

163. Codes from the Skew Ring M_2(F_2) \times_\varphi G,  with S. Sahinkaya, and S. Ustun.

164. Linear Complementary Dual Codes over the p-adic Integers, with E. Salturk.

165. The Neighbor Graph of Linear Codes, with E. Salturk.

166. MacWilliams Relations for Weight Enumerators Given by Equivalnce Relations, with C. Fernandez-Cordoba.

167. The Neighbor Graph of Self-Dual Codes over the Ring of Integers Modulo $4$, with Esengul Salturk.

168. Codes Over an Infinite  Family of Local Rings of Order $2^{5^k}$ with Two Gray Maps, with J. Gildea, A. Korban, and A. Roberts.

169. Additive Self-Dual Codes over Finite Fields, with C. Fernandez-Cordoba and Merce Villanueva.

170. Neighbors of self-dual  codes over the non-commutative ring $E$, with Esengul Salturk.  

171. Graphs of Enhanced Circular Enhanced Permutations, with Sawyer Pappas.  

172. Counting codes over a non-commutative rng, with Esengul Salturk.

Computer Science Publications

173.  Secret sharing schemes based on self-dual codes , Proceedings of IEEE Information Theory Workshop, ITW 2008, Porto, Portugal, with Sihem Mesnager and P. Sole.

174. A Novel Method for Image Encryption Using Time Signature-Dependent S-Boxes Based on Latin Squares and the Playfair System of Cryptography, with S. Sahinkaya and D. Ustun, Multimedia Tools and Applications, DOI 10.1007/s11042-023-15240-0. 

175. An S-Box Construction from Exponentiation in Finite Fields and Its Application in RGB Color Image Encryption, with J. Klobusicky, S. Sahinkaya and D. Ustun, to appear in the Journal of Multimedia Tools and Applications. 

176. An Effective Scheme for Digital Image Encryption Using a Time Signature Based Dynamic S-Boxes,  with S. Sahinkaya and D. Ustun.

177. An S-Box Construction Based on Legendre Symbol and its Application in Image Encryption,  with J. Klobusicky, S. Sahinkaya and D. Ustun.

Other publications

178. Ladder Games, MAA Focus, June/July, 2001, page 25, with Jennifer Franko Vasquez.

179. Shadows of Codes over Rings of Order 4 , presented at the Yamagata Conference, October 2000.

Selected Talks

1. 1. Frobenius Rings,  Autonomous University of Barcelona, Spain, 27 June 2025. 

   2. Characterization of Frobenius Rings, Non-Commutative Rings and their Applications, IX, Lens, France, July 4, 2025.

   3. Codes over Rings and Groups, June 5, 2024, Univeristy of Allicante, Spain.  

   4. Codes and the MacWilliams Relations, Quadratic Forms, Rings, and Codes, Lens France, August 31, 2023.

   5. MacWilliams Relations, UAB, Spain, June 13, 2023. 

   6. Dualities for Finite Groups, Virginia Tech, October 27, 2022.

   7. Foundation of Algebraic Coding Theory, 2021 EIMS International Conference on Computational Mathematics, August 26, 2021.

   8. The Use of Ideals in Coding Theory, Applications of Computer Algebra, July 27, 2021. 

   9. Additive Codes, Non-Commutative Rings and their Applications  VII, July 6, 2021. 

   10. G-Codes over Rings, University of Artois, Lens, June 24, 2019.  

   11. Codes and MacWilliams Relations, Autonomous University of Barcelona, June 19, 2019.

   12. Latin squares, Magic Squares and Tic-Tac-Toe, King's College, November 13, 2018.

   13. A new Fermat Question, Luzerne and Lackawanna Counties Mathematics Symposium, Misericordia University, October 7, 2017.

   14. Circular Permutations, Conference on Mathematics and Games,  Misericordia University, April 9, 2016.

   15. Dualities in Finite Space, Misericordia University, October 3, 2015.

   16. A Practical Guide to the MacWilliams Relations, Universite Artois, Lens, France, June 8, 2015.

   17. Electronic Communication, Football Pools and Hat Color Games, Muhlenberg College, October 17, 2014.

   18. Codes over Rings and Duality, ICM 2014, Ewha University, Seoul, Korea, August 12, 2014.

   19. Codes over Local Rings of Order 16 and their Gray Maps, ACA, Fordham University, New York, USA, July 12, 2014.

   20. Self Dual Codes over Commutative and Non-Commutative Rings, Algebraic Structures and their Applications, Spineto, Italy, 16 June 2014.

   21. Open Questions in Coding Theory, University of Verona, Italy, June 13, 2014.

   22. Self-Dual Codes, University of Verona, Italy, June 12, 2014.

   23. Foundations of Codes over Rings, University of Verona, Italy, June 11, 2014.

   24. Classical Coding Theory, University of Verona, Italy, June 10, 2014.

   25. Une nouvelle question Fermatienne, Université Catholique de Louvain, Louvain la Nouve, Belgium, January 20, 2014 (in French).  

   26. Ladder Problems, Moravian College, November 12, 2013.

   27. Coding Theory and Hadamard Matrices, Misericordia University, September 21, 2013.

   28. Open Problems in Coding Theory, Universite d'Artois, Lens, France, July 1, 2013.

   29. Non-standard Coding Theory, Universite d'Artois, Lens, France, July 2, 2013.

   30. Self-Dual Codes over Frobenius Rings, Universite d'Artois, Lens, France, July 3, 2013.

   31. Classical Coding Theory and Codes over Frobenius Rings, Universite d'Artois, Lens, France, July 4, 2013.

   32. Self-Dual Codes and Codes over Rings, Autonomous University of Barcelona, April 22, 2013.

   33. Japanese Ladders and Games, Eastern Kentucky University Coffee Times Series, February 28, 2013. 

   34. Interesting alphabets and weights for algebraic coding theory, Eastern Kentucky University Discrete Mathematics Seminar, February 27, 2013.

   35. Coding Theory as Pure Mathematics, Eastern Kentucky University Colloquium, February 26, 2013.

   36. Foundations of Algebraic Coding Theory and Avenues of Further Research, ICAAA,  June 22, 2012, Istanbul, Turkey. 

   37. Formally self-dual codes, June 18, ACCT 2012, Pomorie Bulgaria.

   38. Cyclic codes over an infinite family of rings, June 5, 2012, Autonomous University of Barcelona, Spain.

   39. Generalizations  of  the  rings  of  order  4  and  their  Gray  maps, August 24, 2011, International Conference on Coding and Cryptography, Seoul, Korea.

   40. Avenues of research for codes over rings, June 15, 2011, University of Artois, Lens, France.

   41. Coding Theory as Pure Mathematics, Combinatorics Seminar, University of Binghamton, November 16, 2010.

   42. Coding Theory: Pure and Applied, Mathematics Symposium, Misericordia University, September 25, 2010.

   43. The wonderful world of self-dual codes, Discrete Mathematics Day, Misericordia University, September 26, 2009.

   44. Self-dual codes over rings, University of Artois, Lens, France, June 30, 2009.

   45. Coding theory over rings, Autonomous University of Barcelona, Spain, June 23, 2009.

   46. The Nature of Coding Theory, Huangshi Institute of Technology, Huangshi, China, June 5, 2009.

   47. Open Problems in Self-Dual Codes, Huazhong Normal University, Wuhan, China, June 5, 2009.

   48. Advances in Coding Theory - Codes over Rings, Huazhong Normal University, Wuhan, China, June 4, 2009.

   49. Higher Weights for Codes over Rings, AMS special session, Western Michigan University, October 17, 2008.

   50. Codes over rings, AMS special session honoring the retirement of Than Ward, Depaul University, Chicago, IL, October 6, 2007.

   51. The search for the elusive extremal Type II codes, University of Delaware Discrete Mathematics seminar, Deceber 1, 2006.

   52. Optimal Codes over Z_m, Invited lecutre for the 60th Anniversary of the Korean Mathematical Society, Seoul National University, Seoul, Republic of Korea, Oct 27, 2006.

   53. Modular Cyclic codes, AMS conference, Univerity of Cincinnati, Cincinnati Ohio, Oct 21, 2006.

   54. Tic-Tac-Toe on finite planes, CNRS, Sophia-Antipolis, France, March 2, 2006.

   55. Cyclic Codes of even length over the integers modulo 4, SIAM Minisymposium on error-correcting codes, Atlanta, GA, January 5, 2005.

   56. Codes, Lattices and Modular Forms, ITW2003, La Sorbonne, Paris, April 3, 2003.

   57. Constructing Complex and Quaternionic lattices from codes over rings, Combinatorics seminar, University of Binghamton, March 3, 2003.

   58. 36 Officers and Latin Squares, Combinatorics seminar, University of Binghamton, February 20, 2002.

   59. A Coding Theoretic Proof of a Part of the Bruck-Ryser Theorem, Combinatorics seminar, University of Binghamton, October 10, 2001.

   60. Shadows, lattices and codes, POSTECH University, Pohang, South Korea, August 16, 2001.

   61. A very elusive doubly-even code, POSTECH University, Pohang, South Korea, August 16, 2001.

   62. Codes over F_2 + u F_2 and complex lattices, POSTECH University, Pohang, South Korea, August 17, 2001.

   63. The Search for an Extremal Code of Length 72, Combinatorics seminar, University of Binghamton, March 20, 2001.

   64. Codes over Rings and Real Lattices, University of Kiel, Germany, Janaury 16, 2001.

   65. Higher Weights and Binary Self-Dual Codes, WCC2001, Paris, France, January 12, 2001.

   66. Self-Dual Codes and Unimodular Lattices, Lehigh University, November 29, 2000.

   67. Shadows and Space, Combinatorics seminar, University of Binghamton, October 18 and October 25, 2000.

   68. Codes with a non-Hamming metric and Uniform Distributions, International Workshop on Combinatorics, 12th Franco-Japanese Conference, Zao, Japan, October 8, 2000.

   69. Shadows of Codes over Rings of Order 4, Yamagata University, Japan, October 2, 2000.

   70. Codes with a Non-Hamming Metric, AMS Special Topic Session, Notre Dame University, April 8, 2000.

   71. Codes, Lattices and Shadows, Steklov Institute of the Russian Academy of Sciences, March 10, 1999, St. Petersburg, Russia.

   72. Codes of Nets, Vermont Summer Conference of Combinatorics, University of Vermont, June, 1994.

   73. Nets and their Codes, AMS Special Topic Session, Lehigh University, April 1992.

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