Research

My current research interests are in algebraic coding theory with special interest in trellis representations of linear block

codes, subspace codes and MacWilliams identities and extension theorems. I also worked in algebraic systems theory.

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

Ph.D. Students:

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

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

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

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

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

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

7. Isaiah Harney (Ph.D. expected 2017): Colorings of the Hamming graphs

8. Tefjol Pllaha (Ph.D. expected 2018): Extension theorems for sublinear isometries

Membership on Editorial Boards:

1. Linear Algebra and its Applications (2016 - present)

2. SIAM Journal on Applied Algebra and Geometry (2016 - present)

3. Advances in Mathematics of Communications (2006 - present)

4. 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:

1. Journal Publications, Book Chapters, Preprints, and Theses:

2. (with J. Antrobus) Lexicodes over Finite Principal Left Ideal Rings. Preprint 2016. Submitted. ArXiv:1612.04703

3. (with J. Bolkema, C.A. Kelley, K. Lauter, B. Malmskog, J. Rosenthal) Variations of the McEliece Cryptosystem. Preprint 2016. Submitted. ArXiv:1612.05085

4. (with T. Pllaha) Extension theorems for various weight functions over Frobenius bimodules. Preprint 2016. Submitted. ArXiv:1611.01141

5. (with I. Harney) On robust colorings of Hamming-distance graphs. Preprint 2016. Submitted. ArXiv:1609.00263

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

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

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

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

10. (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.

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

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

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

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

223 - 237

1. 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.

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

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

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

5. (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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

20. (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

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

22. 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

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

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

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

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

27. (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

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

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

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

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

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

1. Monograph:

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