Jay Wood's papers on algebraic coding theory

Articles and Refereed Conference Proceedings

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 )

"Foundations of linear codes defined over finite modules: the extension theorem and the MacWilliams identities," which appears in the proceedings volume:  Codes over Rings, Proceedings of the CIMPA Summer School, Ankara, Turkey, 18--29 August 2008, Patrick Solé, editor, Series on Coding Theory and Crytology, Vol. 6, World Scientific, Singapore, 2009, pp. 124--190.  ( pdf )

Anti-isomorphisms, character modules and self-dual codes over non-commutative rings, Int. J. Information and Coding Theory, 1 (4) (2010), 429-444.  (Contained in a special volume in honor of Vera Pless.)     ( pdf )

Applications of Finite Frobenius Rings to the Foundations of Algebraic Coding Theory, in the Proceedings of the 44th Symposium on Ring Theory and Representation Theory (Okayama University, Japan, September 25-27, 2011), O. Iyama, ed., Nagoya, Japan, 2012, pp. 223-245  ( pdf ).

Relative one-weight linear codes, Designs, Codes and Cryptography, 72 (2) (2014), 331-344.  DOI 10.1007/s10623-012-9769-0.  ( pdf ; from the journal, click here )

With Marcus Greferath, Thomas Honold, Cathy Mc Fadden, and Jens Zumbragel, MacWilliams' Extension Theorem for Bi-Invariant Weights over Finite Principal Ideal Rings, J. Combin. Theory, series A, 125C (2014), 177-193.  DOI 10.1016/j.jcta.2014.03.005.  ( pdf ; from the journal, click here )

Some applications of the Fourier transform in algebraic coding theory, in Algebra for Secure and Reliable Communication Modeling, M. Lahyane, E. Martinez-Moro, eds., Contemp. Math. 642, Providence: Amer. Math. Soc., 2015, 1--40.  (CIMPA Research School and Conference, Algebra for Secure and Reliable Communication Modeling, October 1–13, 2012, Morelia, State of Michoacán, Mexico.)  ( pdf ; from the AMS with subscription, click here )

With Noha ElGarem and Nefertiti Megahed, The extension theorem with respect to symmetrized weight compositions, in Coding Theory and Applications, R. Pinto, P. Rocha Malonek, P. Vettori, eds., CIM Series in Mathematical Sciences, vol. 3, Springer, 2015, 177--183.  (4th International Castle Meeting, Palmela Castle, Portugal, September 15--18, 2014.)  ( pdf ; from Springer with subscription, click here )

With Philippe Langevin, The extension problem for Lee and Euclidean weights, J. Algebra Combin. Discrete Appl. 4(2) 2017, 207--217 (proceedings of the 2015 Lens conference NCRA IV).  ( pdf ; from the journal, click here )

With Steve Szabo, Properties of dual codes defined by nondegenerate forms, J. Algebra Combin. Discrete Appl. 4(2) 2017, 105--113 (proceedings of the 2015 Lens conference NCRA IV).  ( pdf ; from the journal, click here )

With Serhii Dyshko and Philippe Langevin, Deux analogues au determinant de Maillet, Comptes Rendus Math. Acad. Sci. Paris. 354 (7) (2016), 649-652. ( pdf )

With Philippe Langevin, The Extension Theorem for the Lee and Euclidean Weights over Z/p^k Z, 2016.  ( pdf )

Isometry groups of additive codes over finite fields, Journal of Algebra and its Applications, to appear.  ( pdf )

Conference Publications 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.  Revised, final version of May 19, 2009:  "Foundations of linear codes defined over finite modules: the extension theorem and the MacWilliams identities."  (See above.)

The use of Frobenius rings in coding theory: a personal view.  Slides for my talk in the special session on Linear Codes over Rings and Modules at the AMS sectional meeting in Kalamazoo, Michigan, October 18, 2008.  (Some of the slides are from the Bloomington talk above.)  ( pdf )

Lecture notes on the MacWilliams identities and the extension theorem, for the CIMAT International School and Conference on Coding Theory, CIMAT, Guanajuato, Mexico, November 28 - December 4, 2008.  Draft version of November 25, 2008 ( pdf ).

Lecture notes on the MacWilliams identities and self-dual codes over non-commutative rings, for the Workshop on Coding Theory and Geometry of Rational Surfaces, Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Michoacán, México, September 23 - 26, 2009.  Draft version of September 23, 2009 ( pdf ).

Ring involutions and self-dual codes. Slides for my talk in the special session on Advances in Algebraic Coding Theory at the AMS sectional meeting in Lexington, Kentucky, March 27, 2010.  ( pdf )  Some photos, courtesy of Jon-Lark Kim: 1 , 2 .

Lecture series:  Two Fundamental Theorems of MacWilliams, Huazhong Normal University, Wuhan, Hubei, China, June-July 2011.  Lecture one, June 22, 2011: The classical case over finite fields ( pdf ).  Lecture two, June 28, 2011: The MacWilliams identities over finite rings ( pdf ).  Lecture three, July 2, 2011:  The MacWilliams extension theorem over finite rings ( pdf ).

The MacWilliams Identities.  Slides for a lecture primarily for undergraduates at the Huangshi Institute of Technology, Huangshi, Hubei, China, June 24, 2011.  ( pdf )

Finite Frobenius Rings as a Setting for Algebraic Coding Theory.  Slides for a lecture at the Hefei University of Technology, Hefei, Anhui, China, June 30, 2011.  ( pdf )

Two lectures on the theme: Applications of Finite Frobenius Rings to Algebraic Coding Theory.  Symposium on Ring and Representation Theory Japan, Okayama University.  Lecture one, September 25, 2011: Two Theorems of MacWilliams over Finite Frobenius Rings ( pdf ).  Lecture two, September 26, 2011:  Using Coding Theory to Characterize Finite Frobenius Rings ( pdf ).  Survey paper prepared for the Symposium: Applications of Finite Frobenius Rings to the Foundations of Algebraic Coding Theory.  (See above.)

Relative One-Weight Codes.  Slides for my talk in the special session on Coding Theory at the AMS sectional meeting in Lincoln, Nebraska, October 14, 2011.  ( pdf )

Characterizing Finite Frobenius Rings Via Coding Theory.  Slides for a lecture in the Algebra and Communications Seminar, University College Dublin, Dublin, Ireland, November 7, 2011.  ( pdf )

Finite Frobenius Rings and the MacWilliams Identities.  Slides for a lecture in the Algebra and Communications Seminar, University College Dublin, Dublin, Ireland, November 14, 2011.  ( pdf )

The MacWilliams Identities.  Slides for the department colloquium at Western Michigan University, Kalamazoo, MI, March 1, 2012.  ( pdf )

Lecture series for the research school Algebra for Secure and Reliable Communication Modeling, Morelia, Michoacan, Mexico, October 2012.  Linear codes over finite rings and modules, October 5, 2012: ( pdf ).  Characters and the MacWilliams identities, October 8, 2012: ( pdf ).  Characters and finite Frobenius rings, October 9, 2012: ( pdf ).  Ring involutions and self-dual codes, October 9, 2012: ( pdf ).  Quasi-cyclic codes, October 12, 2012: ( pdf ).  Equivalence of codes: sufficient conditions, October 12, 2012: ( pdf ).   Equivalence of codes: necessary conditions, October 13, 2012: ( pdf ).  Equivalence of codes: general weights, October 13, 2012: ( pdf ).

Lecture series, Linear codes over finite rings and modules, for the Coding Theory Seminar at Eastern Kentucky University, Richmond, Kentucky, March 2013.  The MacWilliams identities, March 4, 2013: ( pdf ).  The MacWilliams extension theorem over Frobenius rings, March 5, 2013 (Emily day!): ( pdf ).  The MacWilliams extension theorem for general weights, March 6, 2013: ( pdf )

Exotic Automorphisms of Additive Codes.  Slides for my talk in the special session on Algebraic Coding Theory at the AMS sectional meeting in Louisville, Kentucky, October 5, 2013.  ( pdf )

Automorphisms of Additive Codes.  Slides for my talk in the Ring Theory Session of the 32nd Ohio State-Denison Mathematics Conference, Columbus, Ohio, May 9, 2014. ( pdf )

Lecture series (mini-cours), Linear codes from the axiomatic viewpoint, for the conference Noncommutative rings and their applications IV, Lens, France, June 2015.  Overview and characters, June 8, 2015: ( pdf ).  MacWilliams identities, June 8, 2015: ( pdf ).  MacWilliams extension theorem and converse, June 9, 2015: ( pdf ).  MacWilliams extension theorem for other weights, June 9, 2015: ( pdf ).  Isometries of additive codes, June 10, 2015: ( pdf ).  One-weight and relative one-weight codes, June 10, 2015: ( pdf ).  Self-duality for linear codes over modules, June 11, 2015: ( pdf ).  Simplicial complexes coming from linear codes, June 11, 2015: ( pdf ).

Isometry Groups of Additive Codes.  Slides for my talk in the special session on Coding Theory and its Applications at the AMS sectional meeting at Loyola University, Chicago, Illinois, October 4, 2015.  ( pdf )

Mini-course, Foundational aspects of linear codes, for the workshop On the Algebraic and Geometric Classifications of Projective Varieties, Messina, Sicily, June 20-24, 2016.  Characters and Frobenius rings: ( pdf ).  Fourier transform and good duality: ( pdf ). Extension property: sufficient conditions: ( pdf ).  Extension property: necessary conditions: ( pdf ).  Research seminar,  Isometry groups of additive codes: ( pdf ).

The Extension Theorem for Lee Weight.  Slides for my talk in the special session on Advances in Algebraic Coding Theory at the AMS sectional meeting at the University of St. Thomas, Minneapolis, Minnesota, October 29, 2016. (pdf )

Lecture series (course), Character-theoretic tools for studying linear codes over rings and modules, for the CIMPA research school Algebraic Methods in Coding Theory, Ubatuba, Brazil, July 2017.  Linear Codes over Finite Fields, July 3, 2017: ( pdf ).  Additive Codes and Characters, July 4: ( pdf ).  Duality for linear codes, July 5: ( pdf ).  Self-duality for linear codes over modules, July 6: ( pdf ).  MacWilliams extension theorem and converse, July 10: ( pdf ).  MacWilliams extension theorem for other weights, July 11: ( pdf ).  Isometries of additive codes, July 12: ( pdf ).  Using semi-group rings, July 13: ( pdf ).  Extension Problem for general weights, July 14: ( pdf ).

The extension theorem for Lee weight using Dirichlet L-functions.  Slides for my talk in the Algebra Seminar, Department of Mathematics, University of Sao Paulo, Sao Paulo, Brazil, July 17, 2017: ( pdf ).

Groups of isometries of additive codes over GF(q).  Slides for my talk in the special session on Finite Algebraic Combinatorics and Applications, Mathematical Congress of the Americas, Montreal, Quebec, Canada, July 28, 2017: ( pdf ).

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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