My current research interests are in algebraic coding theory with special interest in rank-metric codes, subspace codes and MacWilliams identities and extension theorems. 

I am a member of the algebra group. We run an almost weekly seminar. 

Ph.D. Students:

1. Gert Schneider (PhD  2008): On the weight adjacency matrix of convolutional codes

2. Fai Lung Tsang (PhD 2008): Skew rings, convolutional codes and discrete systems

3. Elizabeth Weaver (PhD 2012): Minimality and duality of tail-biting trellises for linear codes

4. Aleams Barra (PhD 2012): Equivalence theorems and the local-global property

5. Carolyn Troha (PhD 2015): Analysis and Constructions of Subspace Codes

6. Neville Fogarty (PhD 2016): On Skew-Constacyclic Codes

7. Isaiah Harney (PhD 2017): Colorings of Hamming-Distance Graphs

8. Tefjol Pllaha (PhD 2019): Equivalence of Classical and Quantum Codes

9. Jared Antrobus (PhD 2019):  Ferrers-Diagram Codes

10. Hunter Lehmann (PhD 2021): Weight Distribution, Automorphisms, and Isometries of Cyclic Orbit Codes

11. Benjamin Jany (PhD 2023): q-Polymatroids and their Application to Rank-Metric Codes 

12. Kathryn Hechtel: Skew-Cyclic Codes

Membership on Editorial Boards:  

• Linear Algebra and its Applications (2016 - 2022)

• SIAM Journal on Applied Algebra and Geometry (2016 - 2021)

• Advances in Mathematics of Communications (2006 - present)

• SIAM Journal on Control and Optimization (2003 - 2014)

External Funding:

• NSF Grant (Oct 1, 2009 - Sep 30, 2012): $183,418

• NSF Grant (Sep 15, 2012 - Aug 31, 2015): $168,033

• Simons Foundation Collaboration Grant (Sep 1, 2016 - Aug 31, 2021): $35,000

Publications:

Journal Publications, Book Chapters, Preprints, and Theses:     

1. (with B. Jany) Representability of the Direct Sum of q-Matroids. Submitted. ArXiv 2211.11626. 14 pages.

2. (with B. Jany) Decompositions of q-Matroids Using Cyclic Flats. Submitted. ArXiv 2302.02260. 33 pages.

3. (with B. Jany) Coproducts in Categories of q-Matroids. Accepted for Publication in European J. Combinatorics. ArXiv 2111.09723. 23 pages.

4. (with H. Lehmann) Automorphism Groups and Isometries for Cyclic Orbit Codes.  Advances in Mathematics of Communications 17 (2023), 119-138.

5. (with B. Jany) Independent Spaces of q-Polymatroids. Algebraic Combinatorics 5 (2022), 727-744.

6. (with B. Jany) q-Polymatroids and their Relation to Rank-Metric Codes.  Journal of Algebraic Combinatorics 56 (2022), 725-753.

7. (with E. Byrne and A. Ravagnani) Anticodes in the Sum-Rank Metric. Linear Algebra and its Applications 643 (2022), 80-98.

8. (with E. Byrne and A. Ravagnani) Fundamental Properties of Sum-Rank-Metric Codes. IEEE Trans. Inf. Theory 67 (2021), 6456-6475.

9. (with H. Lehmann) Distance Distributions of Cyclic Orbit Codes. Designs, Codes and Cryptography 89 (2021), 447-470.

10. On the Sparseness of Certain MRD Codes. Linear Algebra and its Applications 596 (2020), 145-168. 

11. Skew-Polynomial Rings and Skew-Cyclic Codes. Chapter in "A Concise Encyclopedia of Coding Theory" (eds. Huffman, Kim, Sole), CRC Press 2021 , 151-180.

12. (with A. Ravagnani) Partitions of Matrix Spaces With an Application to q-Rook Polynomials.  European Journal of Combinatorics 89 (2020),  DOI: 10.1016/j.ejc.2020.103120.

13. (with J. Antrobus) Maximal Ferrers Diagram Codes: Constructions and Genericity Considerations, IEEE Trans. Inf. Theory 65 (2019), 6204-6223.

14.  (with T. Pllaha) On quantum stabilizer codes derived from local Frobenius rings.  Finite Fields and Their Applications 58 (2019), 145-173.  

15. (with A.-L. Horlemann-Trautmann) Symbol erasure correction capability of spread codes. IEEE Trans. Inf. Theory 65 (2019), 2075-2091. 

16. (with J. Antrobus) Lexicodes over Finite Principal Left Ideal Rings. Designs, Codes and Cryptography 86 (2018), 2661-2676. 

17. (with J. Bolkema, C.A. Kelley, K. Lauter, B. Malmskog, J. Rosenthal) Variations of the McEliece Cryptosystem. Book chapter in Algebraic Geometry for Coding Theory and Cryptography (Howe E., Lauter K., Walker J. (eds)), Association for Women in Mathematics Series, vol 9. Springer, Cham; 2017. DOI: 10.1007/978-3-319-63931-4 5.

18. (with T. Pllaha) Extension theorems for various weight functions over Frobenius bimodules. Journal of Algebra and Its Applications 17, 2018. DOI: 10.1142/S0219498818500524. 

19. (with I. Harney) On robust colorings of Hamming-distance graphs. The Electronic Journal of Combinatorics, Volume 25, Issue 4 (2018), P4.3.

20. (with C. Troha) Construction of Subspace Codes Through Linkage. Advances in Mathematics of Communications 10 (2016),  525 - 540.

21. (with N. Fogarty) A Circulant Approach to Skew-Constacyclic Codes. Finite Fields and their Applications 35 (2015),  92 - 114.

22. The Homogeneous Weight Partition and its Character-Theoretic Dual. Designs, Codes and Cryptography 79 (2016), 47 -  61.

23. (with K. Morrison and C. Troha) Cyclic Orbit Codes and Stabilizer Subfields. Advances in Mathematics of Communications 9 (2015), 177 - 197.

24. (with A. Barra) MacWilliams Extension Theorems and the Local-Global Property for Codes over Frobenius Rings. Journal of Pure and Applied Algebra 219 (2015), 703 - 728.

25. Partitions of Frobenius Rings Induced by the Homogeneous Weight. Advances in Mathematics of Communications, 8 (2014),       191 - 207.

26. Fourier-Reflexive Partitions and MacWilliams Identities for Additive Codes. Designs, Codes and Cryptography 75 (2015), 543 -   563.

27.  (with G.D. Forney, Jr) Local Irreducibility of Tail-Biting Trellises IEEE Trans. Inf. Theory 59 (2013), 6597-6610.

28.  (with G.D. Forney, Jr) Codes on Graphs: Observability, Controllability and Local Irreducibility, IEEE Trans. Inf. Theory 59 (2013), 223 - 237 

29. On MacWilliams Identities for Codes Over Rings, in: K. Hüper and J. Trumpf  (Ed.), Mathematical System Theory - Festschrift in Honor of Uwe Helmke on the Occasion of his Sixtieth Birthday, CreateSpace, 2013.

30. (with E. Weaver) Characteristic generators and Dualization of Tail-Biting Trellises, IEEE Trans. Inf. Theory 57 (2011), 7418 - 7430

31. (with E. Weaver) Linear Tail-Biting Trellises: Characteristic generators and the BCJR-Construction, IEEE Trans. Inf. Theory 57(2011), 738-751

32. (with U. Helmke and J. I. Iglesias Curto) Algebraic Decoding for Doubly Cyclic Convolutional Codes, Advances in Mathematics of Communications 4(2010), 83-99

33. (with B. Langfeld and W. Schmale) A Short Introduction to Cyclic Convolutional Codes, in: Sala, M.; Mora, T.; Perret, L.; Sakata, S.; Traverso, C. (Ed.), Gröbner Bases, Coding, and Cryptography, RISC Book Series, Springer, Heidelberg (2009), 403-408

34. On isometries for convolutional codes, Advances in Mathematics of Communications 3 (2009), 179-203

35. (with G. Schneider) A MacWilliams Identity for convolutional codes: The general case, IEEE Trans. Inf. Theory 55 (2009), 2920-2930

36. (with F.-L. Tsang) A matrix ring description for cyclic convolutional codes, Advances in Mathematics of Communications 2 (2008), 55-81

37. (with G. Schneider) State space realizations and monomial equivalence for convolutional codes, Linear Algebra and its Applications 425 (2007), 518-533

38. (with G. Schneider) On the MacWilliams Identity for convolutional codes, IEEE Trans. Inf. Theory 54 (2008), 1536-1550

39. On the weight distribution of convolutional codes. Linear Algebra and its Applications 408 (2005), 298-326.

40. (with B. Langfeld) A class of one-dimensional MDS convolutional codes. Journal of Algebra and its Applications 5 (2006), 505-520.

41. (with W. Schmale) On doubly-cyclic convolutional codes. Applicable Algebra in Engineering, Communication and Computing 17 (2006), 151-170.

42. (with B. Langfeld) On the algebraic parameters of convolutional codes with cyclic structures Journal of Algebra and its Applications 5 (2006), 53-76.

43. (with W. Schmale) Distance bounds for convolutional codes and some optimal codes, 2003. 22 pages.

44. (with R. Smarandache und J. Rosenthal) Strongly MDS convolutional codes, IEEE Trans. Inf. Theory 52 (2006), 584-598

45. (with W. Schmale) On cyclic convolutional codes, Acta Applicandae Mathematicae 82 (2004), 183-237

46. (with R. Smarandache und J. Rosenthal) Constructions of MDS-Convolutional Codes, IEEE Trans. Inf. Theory 47 (2001), 2045-2049

47. (with S. Zampieri und P. Vettori) The algebraic structure of DD systems: a behavioral perspective, Kybernetika 37 (2001), 397-426

48. (with J. Rosenthal und P. Weiner) Duality between Multidimensional Convolutional Codes and Systems, in: F. Colonius, U. Helmke, F. Wirth, D. Praetzel-Wolters (Ed.), Advances in Mathematical Systems Theory, Birkhauser Boston, 2000, 135-150

49. The Fuhrmann-realization for multi-operator systems in the behavioral context , Multidimensional Systems and Signal Processing 11 (2000), 193-211

50. A convolution algebra of delay-differential operators and a related problem of finite spectrum assignability, Mathematics of Control, Signals, and Systems 13 (2000), 22-40

51. First-order representations of delay-differential systems in a behavioural setting, European Journal of Control 3 (1997), 137-149

52. A behavioral approach to delay-differential systems, SIAM Journal on Control and Optimization 35 (1997), 480-499

53. Continuous state-representations for AR-systems, Mathematics of Control, Signals, and Systems 8 (1995), 82-95

54. Realization of rational matrices by singular systems, Journal of Mathematical Systems, Estimation, and Control 5 (1995), no. 1, 1-32

55. (with F. De Mari) The spaces of improper rational matrices and ARMA-systems of fixed McMillan degree, Journal of Mathematical Systems, Estimation, and Control 5 (1995), no. 1, 1-19

56. (with D. Hinrichsen) The degeneration of reachable singular systems under feedback-transformations, Kybernetika 30 (1994), 387-391

57. On various topologies for finite-dimensional linear systems, Institute for Dynamical Systems, University of Bremen, Report No. 273, December 1992, 39 pages

58. Gruppenaktionen in der Theorie singulärer Systeme, Dissertation, University of Bremen, 1991

59. Feedback canonical form for singular systems, International Journal of Control 52 (1990), 347--376

60. (with D. Hinrichsen) A Jordan control canonical form for singular systems, International Journal of Control 48 (1988), 1769-1785

Monograph:

1. Linear Delay-Differential Systems with Commensurate Delays: An Algebraic Approach; Lecture Notes in Mathematics 1770; Springer 2002.