Jay Wood's papers on algebraic coding theory

Articles

Spinor groups and algebraic coding theory, J. Combin. Theory, series A, 50 (1989) 277--313.

Maximal abelian subgroups of spinor groups and error-correcting codes, in Algebraic Topology, Mark Mahowald, Stewart Priddy, eds., Contemporary Mathematics, vol. 96, 1989, pp. 333--350.

Self-orthogonal codes and the topology of the spinor groups, in Coding Theory and Design Theory, Part I, Coding Theory, D. Ray-Chaudhuri, ed., IMA volumes in Mathematics and its Applications, volume 20, Springer-Verlag, New York, 1990, pp. 219--239.

Witt's extension theorem for mod four valued quadratic forms, Trans. Amer. Math. Soc., 336 (1993) 445--461.

With Harold N. Ward , Characters and the equivalence of codes, J. Combin. Theory, series A, 73 (1996) 348--352.

Extension theorems for linear codes over finite rings, in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, T. Mora, H. Mattson, eds., LNCS 1255, Berlin: Springer-Verlag, 1997, pp. 329--340. (Proceedings of 12th International Symposium, AAECC-12, Toulouse, France, June 23--27, 1997.) ( dvips , pdf )

Weight functions and the extension theorem for linear codes over finite rings, in Finite Fields: Theory, Applications and Algorithms,  R. C. Mullin, G. L. Mullen, eds., Contemp. Math. 225, Providence: Amer. Math. Soc., 1999, 231--243. (Proceedings of the Fourth International Conference on Finite Fields: Theory, Applications and Algorithms, August 12--15, 1997, University of Waterloo, Waterloo, Ontario, Canada.) ( dvi , ps , pdf )

Duality for modules over finite rings and applications to coding theory, Amer. J. Math., 121 (1999), 555-575. ( dvi , ps , pdf ; also, pdf version available from Amer. J. Math for subscribers to MUSE)

Factoring the semigroup determinant of a finite commutative chain ring, in Coding Theory, Cryptography and Related Areas, J. Buchmann, T. Hoholdt, H. Stichtenoth, and H. Tapia-Recillas, eds., Springer-Verlag, Berlin, 2000, pp. 249--259.  (Proceedings of the International Conference on Coding Theory and Cryptography, Guanajuato, Mexico, 1998.)       ( dvi , ps , pdf )

The structure of linear codes of constant weight, Trans. Amer. Math. Soc. 354 (2002), 1007-1026. ( pdf  ; from the AMS, click  here .)

Code equivalence characterizes finite Frobenius rings,  Proc. Amer. Math. Soc. 136 (2008), 699-706.   ( pdf ; from the AMS, click here .)  An earlier, longer version of the paper: A coding-theoretic characterization of finite Frobenius rings, manuscript dated February 28, 2006.  ( pdf )

Conference Proceedings and Presentations

Semigroup rings and the extension theorem for linear codes, Proceedings of the Thirty-Fifth  Annual Allerton Conference on Communication, Control, and Computing, University of Illinois, 1997, pp. 163--172. (Preliminary version of the "Weight functions" paper.) ( dvi , ps , pdf )

Codes of constant Lee or Euclidean weight, extended abstract for the Workshop on Coding and Cryptography , Paris, 1999. ( dvi , ps , pdf )   Slides for my talk. ( dvi , ps , pdf )

Witt theorems for linear codes over finite Frobenius rings.  These are slides of my talk at the International Conference on Algebra and its Applications, Athens, Ohio, March 27, 1999.           ( dvi , ps , pdf )

Linear codes over Z/(2^k) of constant Euclidean weight, Proceedings of the Thirty-Seventh Annual Allerton Conference on Communication, Control, and Computing, University of Illinois, 1999, pp. 895--896.  ( dvi , ps , pdf )   Slides for my talk.  ( dvi , ps , pdf )  Finally, a long version of the paper containing material on orbit structures and a uniqueness theorem. ( dvi , ps , pdf )

Understanding linear codes of constant weight using virtual linear codes, Proceedings of the Thirty-Eighth Annual Allerton Conference on Communication, Control, and Computing, University of Illinois, 2000, pp. 1038--1046.  ( pdf )   Slides for my talk.  ( pdf )

The structure of linear codes of constant weight, Proceedings of the International Workshop on Coding and Cryptography ,  D. Augot, C. Carlet, eds., INRIA, Paris, 2001, pp. 547--556.  ( pdf )  Slides for my talk. ( pdf )

The development of coding theory over finite rings.  Slides for my talk in the special session on Algebraic Coding Theory at the Joint Mathematics Meetings, San Diego, California, January 7, 2002.  ( pdf )

Restrictions on two-weight projective linear codes.  Proceedings of the International Workshop on Coding and Cryptography , INRIA,  Versailles, March 24-28, 2003.  ( N/A )  Slides for my talk, March 28, 2003. ( pdf )

An essay on equivalence of linear codes.  Slides for my talk in the special session on Applications of Number Theory and Algebraic Geometry to Coding at the AMS sectional meeting in Boulder, Colorado, October 4, 2003.  ( pdf  )

A essay on equivalence of linear codes, II.  Slides for my talk in the special session on Algebraic Coding Theory at the AMS sectional meeting in Athens, Ohio, March 26, 2004.  ( pdf  )

A essay on equivalence of linear codes, III.  Slides for my talk in the special session on Coding Theory and Cryptography at the AMS/SMM international joint meeting in Houston, Texas, May 14, 2004.  (  pdf  )

Highly symmetric weight functions on matrix rings.  Slides for my talk in the special session on Codes and Applications at the AMS sectional meeting in Evanston, Illinois, October 23, 2004.  ( pdf )

Code equivalence and finite Frobenius rings.  Slides for my talk in the Theory of Rings and Modules section of the 28th Ohio State-Denison Conference, Columbus, Ohio, May 19, 2006.  ( pdf )

Equivalence of linear codes over finite rings (in honor of Vera Pless).  Slides for my talk in the special session on Algebraic Coding Theory---Honoring the Retirement of Vera Pless at the AMS sectional meeting in Cincinnati, Ohio, October 22, 2006.  ( pdf )

Character-theoretic proofs of equivalence theorems (in honor of Thann Ward).  Slides for my talk in the special session on Algebraic Coding Theory (in honor of Harold N. Ward's retirement) at the AMS sectional meeting in Chicago, Illinois, October 6, 2007.  ( pdf )

Dual codes over finite rings---cautions and compromises.  Slides for my talk in the special session on Algebraic Aspects of Coding Theory at the AMS sectional meeting in Bloomington, Indiana, April 5, 2008.  ( pdf )

Lecture notes on linear codes defined over finite modules: the extension theorem and the MacWilliams identities.  Draft version of August 14, 2008 ( pdf ).  For the use of the CIMPA-UNESCO-TUBITAK Summer School on Codes over Rings, Middle East Technical University, Ankara, Turkey, August 18-29, 2008.

Other

Arithmetic progressions of constant $p$-adic weight, 2001.  ( pdf )

The chain rule for matrix exponential functions, College Math J. 35 (2004), 220-222.  ( pdf )



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