Publications


Publications of Steven Dougherty





The following are in print.


  1. Nets and their codes, Designs, Codes and Cryptography, 3, 315-331, 1993.
  2. A Coding-Theoretic Solution to the 36 Officer Problem , Designs, Codes and Cryptography, 4, 123-128, 1994.
  3. Shadow Codes and their Weight Enumerators , IEEE Transactions on Information Theory, Volume 41, Number 3, May 1995.
  4. Extremal Binary Self-dual Codes, IEEE Transactions on Information Theory, 2036-2047, November 1997, with M. Harada and T.A. Gulliver.
  5. Planes, Nets and Codes , Mathematical Journal of Okayama University Vol 38, December 1996.
  6. 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.
  7. Optimal Ternary Formally Self-dual Codes, Discrete Mathematics 196, 1999, 117-135, with T.A. Gulliver an M. Harada.
  8. 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.
  9. Self-Dual Codes over Rings and the Chinese Remainder Theorem, Hokkaido Math Journal, Volume 28, 1999, 253-283, with M. Harada and P. Sole.
  10. 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.
  11. Shadow Optimal Self-Dual Codes, Kyushu Journal of Mathematics, Vol 53, No. 2., 1999, p. 223-237, with M. Harada.
  12. 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.
  13. MDR Codes over Z_k , IEEE-IT, Vol 46, No. 1, January 2000, p. 265-269, with Keisuke Shiromoto.
  14. New Extremal Codes of Length 68 , IEEE-IT, Vol 46, No. 6, 2133-2136, September 1999, with M. Harada.
  15. Self-Dual Codes and Finite Projective Planes , Mathematical Journal of Okayama University, Vol. 40, 1998,2000.
  16. Shadow Lattice and Shadow Codes, Discrete Math, Vol. 219 (2000), 49-64, with M. Harada and P. Sole.
  17. 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.
  18. Maximum Distance Codes over Rings of Order 4, IEEE-IT, Vol 47, No 1, January 2001, with Keisuke Shiromoto.
  19. 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.
  20. Higher Weights and Binary Self-Dual Codes , Electronic Notes in Applied Mathematics, April, 2001, with T. Aaron Gulliver.
  21. Shadow Codes over Z_4 , Finite Fields and their Applications, Vol. 7, No. 4, (2001), 507-529, with M. Harada and P. Sole.
  22. MacWilliams Duality and the Rosenbloom-Tsfasman Metric, Moscow Mathematical Journal, Vol. 2, Number 1, 2002, 83-99, with M.M. Skriganov.
  23. 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.
  24. 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.
  25. 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.
  26. Generalized Shadows of Codes over Rings, Hokkaido Mathematical Journal, Vol XXXII, No 1, February 2003, 101-116.
  27. 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.
  28. Splitting the Shadow , Discrete Mathematics 270, 2003, 43-60, with A. Bonnecaze, Y. Choie and P. Sole.
  29. 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.
  30. 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.
  31. Tic-Tac-Toe on a Finte Plane , Math Magazine, 260-274, October 2004, with Maureen Carroll. (Awarded Hasse Prize 2005).
  32. Codes over Sigma_{2m} and Jacobi Forms over the Quaternions , Appl. Algebra. Engr. Com. Comput. 15, 2004 No. 2, 129-147, with YoungJu Choie.
  33. Generalized Weights for Codes over Finite Rings, AJC, 31, 2005, 231-248, with M. Gupta and K. Shiromoto.
  34. A New Construction of Self-Dual Codes from Projective Planes, AJC, 31, 2005, 337-348.
  35. Codes over Rings, Complex Lattices, and Hermitian Modular Forms, European Journal of Combinatorics, 26, 2005, No. 2, 145-165, with YoungJu Choie.
  36. Complete Joint Weight Enumerators and Self-Dual Codes , IEEE-IT, 49, No. 5, 2003, 1275-1282, with Young Ju Choie and Haesuk Kim.
  37. Lifted Codes and their Weight Enumerators, Discrete Mathematics, 305, Vol 1-3, 2005, 123-135, with Young Ho Park and Sun Young Kim.
  38. Higher Weights for Ternary and Quaternary Self-Dual Codes , Designs, Codes and Cryptography, 38, 97-112, 2006, with T. Aaron Gulliver and Manabu Oura.
  39. Codes over the p-adic integers, Designs, Codes and Cryptography, April 2006, 65-80, with Young Ho Park.
  40. Cyclic codes over Z_4 of even length , Designs, Codes and Cryptography, May 2006, 127-153, with San Ling.
  41. Double Circulant Codes from Two Class Association Schemes, with Jon-Lark Kim and P. Sole, AMC, Volume 1, Number 1.
  42. Self-dual codes over Z_8 and Z_9 , Designs, Codes and Cryptography, 41, 235-249, 2006, with T. Aaron Gulliver and John Wang.
  43. On Modular Cyclic Codes , Finite Fields and their Applications Volume 13, Number 1, 31-57, 2007, with Young Ho Park.
  44. 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.
  45. Symmetric Designs and Self-Dual Codes over Rings , Ars Combinatoria, Vol. 85, 2007, with Aaron Gulliver and Reshma Ramadurai.
  46. Latin k-hypercubes, AJC, Volume 40, February 2008, with T. Szczepanski.
  47. Higher Weights of Codes from Projective Planes and Biplanes, Mathematical Journal of Okayama University, Vol. 49, 2007, with Reshma Ramadurai.
  48. The nature of coding theory, News Letter of the Korean Mathematical Society, July 2007, 26-31. (appears in Korean)
  49. MDS codes over finite principal ideal rings , Designs, Codes and Cryptography, Volume 50, 77-92, 2009, with Jon-Lark Kim and Hamid Kulosman.
  50. Independence of vectors in codes over rings, Designs, Codes and Cryptography, 55-68, 2009, with Hongwei Liu.
  51. Type II codes over finite rings , Science in China, Volume 53, Number 1, 203-212, with Hongwei Liu.
  52. 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.
  53. 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.
  54. Lifted Codes over Finite Chain Rings , with Hongwei Liu and Young Ho Park, Mathematical Journal of Okayama University Volume 53, January 2010, 39-53.
  55. Cyclic Codes over Formal Power Series , with Hongwei Liu, Acta Mathematica Scientia 2010, 31 B (1): 331-343.
  56. Higher Weights and Generalized MDS codes , with Sunghyu Han, Korean Mathematical Society, Volume 47, Number 6, 2010, 1167-1182.
  57. Higher Weights for Codes over Rings , Applicable Algebra in Engineering, Communication and Computing, with Sunghyu Han and Hongwei Liu.
  58. 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.
  59. 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.
  60. 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.
  61. Cyclic Codes over R_k , with Bahattin Yildiz and Suat Karadeniz,  Designs, Codes and Cryptography, Volume 63, Number 1.
  62. Self-Dual codes over Z2 x Z4 , with J. Borges and Cristina Fernandez-Cordoba, AMC, Volume 6, Number 4, 287-303, 2012.
  63. Amidakuji and Games, with Jennifer Franko Vasquez,  Journal of Recreational Mathematics, Volume 37 (1), 46-56, 2008.
  64. Z_2Z_4-Additive Formally Self-Dual Codes, with C. Fernandez-Cordoba,  Designs, Codes and Cryptography, Dec. 2012.
  65. 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.
  66. 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.
  67. Counting Codes over Rings, Designs, Codes and Cryptography,  2013,   with Esengul Salturk.
  68. Indivisibles, infinitesimals and a tale of seventeenth century mathematics, Mathematics Magazine, 86 (2013, no. 4, 239-254, with M.T. Carroll and Dave Perkins.
  69. Constructing Formally Self-Dual Codes over R_k, with Bahattin Yildiz and Suat Karadeniz,  Discrete Applied Mathematics, December 2013. 
  70. Linear Codes, Hermitian Lattices, and Finite Rings, with Jon-Lark Kim and Yoonjin Lee,   Designs, Codes and Cryptography, 2014.
  71. 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.


  72. The following appear as a book chapter.

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

    The following appear in a refereed proceedings.

  74. 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).
  75. Codes, Lattices and Modular Forms , Proceedings of the 2003 IEEE Information Theory Workshop, 259-262, with Young Ju Choie.
  76. Secret sharing schemes based on self-dual codes , Proceedings of IEEE Information Theory Workshop, ITW 2008, Porto, Portugal, with Sihem Mesnager and P. Sole.
  77. Optimal codes over Z2 X Z4, JMDA 2010, with M. Bilal, J. Borges, and C. Fernandez-Cordoba.
  78. Additive Codes over Z2 x Z4, ITW 2010, Dublin, with J. Borges, and C. Fernandez-Cordoba.
  79. Binary self-dual codes from 3-class association schemes, 3ICMCTA, with M. Bilal, J. Borges, and C. Fernandez-Cordoba. 
  80. Formally self-dual codes and Gray maps, to appear at ACT2012, Pomorie, Bulgaria.
  81. Cyclic codes over A_k, to appear at ACCT2012, Pomorie, Bulgaria, with Yasemine Cengellenmis.
  82. Extensions of Z2Z4 Additive Self-Dual Codes Preserving Their Properties,   ISIT 2012, with M. Bilal, J. Borges, and C. Fernandez-Cordoba.
  83. The following are to appear.

  84. Foundations of Algebraic Coding Theory, to appear in Contemporary Mathematics.
  85. Counting Additive Z2Z4 codes, with Esengul Salturk to appear in Contemporary Mathematics.
  86. Open Problems in Coding Theory, with Jon-Lark Kim and P. Sole, to appear in Contemporary Mathematics.

  87. The following are in submission.


  88. Self-dual codes from 3-class association schemes, with M. Bilal, J. Borges and C. Fernandez-Cordoba.
  89. Japanese Ladders and the Braid Group, with Michael Allocca and Jennifer Vasquez.
  90. On codes over Z_{p^e} with extended Lee weight, with Zeynep Ozger and Bahattin Yildz.
  91. Self-dual codes over non-commutative Frobenius rings, with André Leroy.  
  92. One weight Z2Z4 additive codes, with Hongwei Liu and Long Yu. 
  93. Generalized Additive Codes, Self-Dual Codes and Formally Self-Dual Codes, with Hongwei Liu.
  94. On the duality and the direction of polycyclic codes, with Adel Alahamdi, Andre Leroy and Patrick Sole.
  95. Other publications.

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

Other papers


Selected Talks

  1. Self Dual Codes over Commutative and Non-Commutative Rings, Algebraic Structures and their Applications, Spineto, Italy, 16 June 2014.
  2. Open Questions in Coding Theory, University of Verona, Italy, June 13, 2014.
  3. Self-Dual Codes, University of Verona, Italy, June 12, 2014.
  4. Foundations of Codes over Rings, University of Verona, Italy, June 11, 2014.
  5. Classical Coding Theory, University of Verona, Italy, June 10, 2014.
  6. Une nouvelle question Fermatienne, Université Catholique de Louvain, Louvain la Nouve, Belgium, January 20, 2014 (in French).  
  7. Ladder Problems, Moravian College, November 12, 2013.
  8. Coding Theory and Hadamard Matrices, Misericordia University, September 21, 2013.
  9. Open Problems in Coding Theory, Universite d'Artois, Lens, France, July 1, 2013.
  10. Non-standard Coding Theory, Universite d'Artois, Lens, France, July 2, 2013.
  11. Self-Dual Codes over Frobenius Rings, Universite d'Artois, Lens, France, July 3, 2013.
  12. Classical Coding Theory and Codes over Frobenius Rings, Universite d'Artois, Lens, France, July 4, 2013.
  13. Self-Dual Codes and Codes over Rings, Autonomous University of Barcelona, April 22, 2013.
  14. Japanese Ladders and Games, Eastern Kentucky University Coffee Times Series, February 28, 2013. 
  15. Interesting alphabets and weights for algebraic coding theory, Eastern Kentucky University Discrete Mathematics Seminar, February 27, 2013.
  16. Coding Theory as Pure Mathematics, Eastern Kentucky University Colloquium, February 26, 2013.
  17. Foundations of Algebraic Coding Theory and Avenues of Further Research, ICAAA,  June 22, 2012, Istanbul, Turkey. 
  18. Formally self-dual codes, June 18, ACCT 2012, Pomorie Bulgaria.
  19. Cyclic codes over an infinite family of rings, June 5, 2012, Autonomous University of Barcelona, Spain.
  20. Generalizations  of  the  rings  of  order  4  and  their  Gray  maps, August 24, 2011, International Conference on Coding and Cryptography, Seoul, Korea.
  21. Avenues of research for codes over rings, June 15, 2011, University of Artois, Lens, France.
  22. Coding Theory as Pure Mathematics, Combinatorics Seminar, University of Binghamton, November 16, 2010.
  23. Coding Theory: Pure and Applied, Mathematics Symposium, Misericordia University, September 25, 2010.
  24. The wonderful world of self-dual codes, Discrete Mathematics Day, Misericordia University, September 26, 2009.
  25. Self-dual codes over rings, University of Artois, Lens, France, June 30, 2009.
  26. Coding theory over rings, Autonomous University of Barcelona, Spain, June 23, 2009.
  27. The Nature of Coding Theory, Huangshi Institute of Technology, Huangshi, China, June 5, 2009.
  28. Open Problems in Self-Dual Codes, Huazhong Normal University, Wuhan, China, June 5, 2009.
  29. Advances in Coding Theory - Codes over Rings, Huazhong Normal University, Wuhan, China, June 4, 2009.
  30. Higher Weights for Codes over Rings, AMS special session, Western Michigan University, October 17, 2008.
  31. Codes over rings, AMS special session honoring the retirement of Than Ward, Depaul University, Chicago, IL, October 6, 2007.
  32. The search for the elusive extremal Type II codes, University of Delaware Discrete Mathematics seminar, Deceber 1, 2006.
  33. 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.
  34. Modular Cyclic codes, AMS conference, Univerity of Cincinnati, Cincinnati Ohio, Oct 21, 2006.
  35. Tic-Tac-Toe on finite planes, CNRS, Sophia-Antipolis, France, March 2, 2006.
  36. Cyclic Codes of even length over the integers modulo 4, SIAM Minisymposium on error-correcting codes, Atlanta, GA, January 5, 2005.
  37. Codes, Lattices and Modular Forms, ITW2003, La Sorbonne, Paris, April 3, 2003.
  38. Constructing Complex and Quaternionic lattices from codes over rings, Combinatorics seminar, University of Binghamton, March 3, 2003.
  39. 36 Officers and Latin Squares, Combinatorics seminar, University of Binghamton, February 20, 2002.
  40. A Coding Theoretic Proof of a Part of the Bruck-Ryser Theorem, Combinatorics seminar, University of Binghamton, October 10, 2001.
  41. Shadows, lattices and codes, POSTECH University, Pohang, South Korea, August 16, 2001.
  42. A very elusive doubly-even code, POSTECH University, Pohang, South Korea, August 16, 2001.
  43. Codes over F_2 + u F_2 and complex lattices, POSTECH University, Pohang, South Korea, August 17, 2001.
  44. The Search for an Extremal Code of Length 72, Combinatorics seminar, University of Binghamton, March 20, 2001.
  45. Codes over Rings and Real Lattices, University of Kiel, Germany, Janaury 16, 2001.
  46. Higher Weights and Binary Self-Dual Codes, WCC2001, Paris, France, January 12, 2001.
  47. Self-Dual Codes and Unimodular Lattices, Lehigh University, November 29, 2000.
  48. Shadows and Space, Combinatorics seminar, University of Binghamton, October 18 and October 25, 2000.
  49. Codes with a non-Hamming metric and Uniform Distributions, International Workshop on Combinatorics, 12th Franco-Japanese Conference, Zao, Japan, October 8, 2000.
  50. Shadows of Codes over Rings of Order 4, Yamagata University, Japan, October 2, 2000.
  51. Codes with a Non-Hamming Metric, AMS Special Topic Session, Notre Dame University, April 8, 2000.
  52. Codes, Lattices and Shadows, Steklov Institute of the Russian Academy of Sciences, March 10, 1999, St. Petersburg, Russia.
  53. Codes of Nets, Vermont Summer Conference of Combinatorics, University of Vermont, June, 1994.
  54. Nets and their Codes, AMS Special Topic Session, Lehigh University, April 1992.


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