# Research

## Error-correcting codes page

A webpage on error-correcting codes

## Research Publications:

- "A note on gaps between zeroes of L-functions," unpublished preprint dating from 1984.
- "Summation operators and 'explicit formulas'", Port. Math.
**44**(1987)119-130. pdf - "On the metaplectic analog of Kazhdan's 'endoscopic' lifting", Isr. J. Math.
**61**(1988)113-154.

preprint version - "On the Kuznetsov-Bruggeman Formula for a Hilbert Modular Surface Having One Cusp", Math. Zeit.
**203**(1990)59-104, Errata, Math. Zeit.**205**(1990)163.

Corrected version - "On twisted orbital integral identities for PGL(3) over a p-adic field", Can. J. Math.
**31**(1991)1098-1130.

preprint version - "On the Montgomery-Dyson hypothesis", in Proceedings of the Amalfi Analytic Number Theory Conference, Univ. de Salerno, 1992.
- "Remarks on the Bruggeman-Kutznetsov formula", Proceedings of the Amalfi Analytic Number Theory Conference, Univ. de Salerno, 1992.
- "Simple local trace formulas for unramified p-adic groups", Pac. J. Math.
**154**(1992)103-129.

corrected preprint version(pdf only - sorry, the source file seems to have been lost) - with Roland Martin, "Decomposing Lie Algebra Representations Using Crystal Graphs", SAC Newsletter, no. 2, June 1997, pp. 27-34.
- preprint version
- with R. Martin, "Using crystal graphs to decompose Lie algebra representations", SIGSAM Bull
**31**Dec. 1997. - with R. Martin, "Branching rules for Lie algebra representations using crystal graphs", Maple Tech
**25**(1998)23-27. preprint version - "A correspondence for the generalized Hecke algebra of the metaplectic cover of SL(2,F), F p-adic," New York J of Math.
**4**(1998) 223-235. On the NYJM web page - with David Jabon, "On stable characters of tamely ramified supercuspidal representations of small unitary groups", Far East J. of Math. Sci.,
**1**(1999)443-454

preprint version. - "On the unitary dual of $\overline{SL(2,F)}, F p-adic," unpublished preprint, 1999.
- "A correspondence for the supercuspidal representations of the metaplectic cover of SL(2,F), F p-adic," Archiv der Math. vol 73(1999)332-340
- "On finite dimensional representations of non-connected reductive groups," J. of Lie Theory.
**10**(2000)269-284. On the JLT web page - "Invariant distributions on the n-fold metaplectic covers of GL(r,F), F p-adic," J. Fourier Anal. and Appl.
**7**(2001)343-358.

preprint version - with Salahoddin Shokranian, "Remarks on codes from Goppa curves: MAPLE applications," in
**Coding Theory and Cryptography: From Enigma and Geheimschreiber to Coding Theory**, Springer-Verlag, 2000. citeseer (there is a Magma version at the math arXivs - with Dennis Spellman, Georgia M. Benkart, Anthony M. Gaglione, Mark E. Kidwell, Mark D. Meyerson and William P. Wardlaw, "Principal ideals and associate rings," JP Journal of Algebra, number theory, and applications
**2**(2002)181-193.

preprint version - "Representations of finite groups on Riemann-Roch space of a toric variety," preprint, 2002.
- with Michael Fourte, "Odd King Tours on Even Chessboards," Journal of Recreational Mathematics
**31**(2003)173-177.

preprint version - "Arithmetic of characters of generalized symmetric groups," Archiv der Mathematik, vol 81 (2003)113--120.

preprint version 1, preprint version 2 - with Helena Verrill, "Notes on toric varieties," preprint at math arxivs and preprint (the latter version contains an index). "Computing with toric varieties,"
*J. Symb. Comp.*Volume 42 (2007)511-532 . - "Toric codes over finite fields", AAECC, vol. 15, Number 1 (2004)63 - 79. A version may be found at math arXivs
- with Will Traves, "Representations of finite groups on Riemann-Roch spaces," available at math arXivs.
- with Pablo Legarraga, "Smoothness Properties of Varieties of Borels and Schubert Varieties," (appeared in Revista UMA, vol. 45, 2004, pp 69-74). A similar version (using different methods) under the title "On the variety of Borels in relative position
**w**" is available at math arXivs. - with Amy Ksir, "Representations of finite groups on Riemann-Roch spaces, II" is available at math arxivs. (published version was renamed "Decomposing representations of finite groups on Riemann-Roch spaces" Proc. Amer. Math. Soc. 135 (2007), 3465-3476. )
- (with Amy Ksir) "Automorphism groups of some AG codes"
*IEEE Trans. Info. Theory*, vol 52, July 2006, pp 3325-3329.

IEEE version, math arXiv version. - "Open Source Computer Algebra Systems - Maxima", ACM Communications in Computer Algebra, Volume 40, Number 3/4 - September/December 2006 - Issue 157/158.
- with Robert Guralnick and Daniel Goldstein, "A Question about Pic(X) as a G-module," is available at math arXivs. (
**Computational Aspects of Algebraic Curves**, (Editor: T. Shaska) Lecture Notes in Computing, WorldScientific, 2005.) - with Alexander Konovalov, "Applications of the computer algebra system GAP in coding theory,"
*2nd International conference Modern coding methods in electronic systems*October 26-27, 2004, Sumy, Ukraine. Abstracts. Sumy University Publishers, Sumy, 2004. Pages 18-19. It is available, but only in Russian (or is it Ukranian?), and as a pdf file. - "Conjectural permutation decoding of some AG codes"
*Communications in Computer Algebra (formerly "SIGSAM Bull"),*vol 39, March 2005, pages 166-172. - (with Amy Ksir) "Modular representations on some Riemann-Roch spaces of modular curves X(N)" (
**Computational Aspects of Algebraic Curves**, (Editor: T. Shaska) Lecture Notes in Computing, WorldScientific, 2005.) - (with S. McMath, F. Crabbe) "Continued fractions and Parallel SQUFOF",
*International Journal of Pure and Applied Mathematics*volume 34, Number 1 (2007)19-38. See math arXivs. - (with William Stein) "SAGE: System for Algebra and Geometry Experimentation",
*Communications in Computer Algebra,*vol 39, June 2005, pages 61-64. *"GUAVA: An error-correcting codes package" Communications in Computer Algebra, vol 39, June 2005, pages 65-68.*- (with Amy Ksir, Tony Shaska) "Bases for Riemann-Roch spaces of hyperelliptic curves," preprint, 2006. Partially implemented in SAGE.
- "Mathematics of Ghaly's machine",
*Integers.* - "Quadratic residue codes and hyperelliptic curves", preprint math arxivs. Discrete Mathematics and Theoretical Computer Science, vol 10(2008) 129-146.
- "Open Source Computer Algebra Systems - Axiom", ACM Communications in Computer Algebra, Volume 42, Number 2 - June 2008 - Issue 164.
- (with Amy Ksir, Will Traves) "Automorphism groups of GRS codes" in .
**Advances in coding theory and cryptology**, (T. Shaska, W. C. Huffman, D. Joyner, V. Ustimenko, editors), World Scientific, 2007. See math arXivs. - (with Amy Ksir, Roger Vogeler) "Group representations on Riemann-Roch spaces of some Hurwitz curves"
*Albanian Journal of Mathematics,*Volume 1, Number 2 (2007)67-85 (electronic version). math arXivs. - "A primer on computational group homology and cohomology." See arXivs. To appear in the Proceedings of the Gaglione conference, entitled
**Aspects of Infinite Groups**(ed. Ben Fine), published by World Scientific Press. - (with David Kohel) "Groups and SAGE", in
**Computational Group Theory and the Theory of Groups**, AMS "Contemporary Mathematics" series vol. 470 (ed. Luise-Charlotte Kappe, Arturo Magidin, Robert Morse), 2008, pp. 115-140. (Here is thesource tarball.) - with Amy Ksir and Darren Glass, "Codes from Riemann-Roch spaces for
*y2 = xp-x*over GF(p)", Accepted for publication in**Algebraic and Combinatorial Coding Theory in Honour of the Retirement of Vera Pless**, a special issue of*International. J. of Information and Coding Theory*, (editors: Philippe Gaborit, Jon-Lark Kim, Patrick Sole, and Isaac Woungang). - with Amy Ksir and Caroline Melles, "Automorphism Groups on Tropical Curves: Some Cohomology Calculations." Beitrage zur Algebra und Geometrie, Volume 53, Issue 1 (2012), Page 41-56.
- with Chris Christensen and Jenna Torres, "Lester Hill's error-detecting codes", Cryptologia, 2011.
- with Ondrej Certik, Aaron Meurer, Brian Granger, "Open Source Computer Algebra Systems: SymPy" to appear in ACM Communications in Computer Algebra, (2011, December).
- with Charles Celerier, Caroline Melles, David Phillips, "On the Walsh-Hadamard transform of monotone Boolean functions" in
**Tbilisi Mathematical Journal**Special Issue on Sage and Research - with Charles Celerier, Caroline Melles, David Phillips, Steven Walsh "Edge-weighted Cayley graphs and p-ary bent functions", to appear in INTEGERS

## Books:

**Distribution theorems of L-functions**, Pitman Research Notes, vol 142, Longman Scientific and Technical, 1986. See also errata.- with G. Nakos,
**Linear algebra and its applications**, Brooks-Cole (ITP), 1998. - (editor)
**Coding Theory and Cryptography: From Enigma and Geheimschreiber to Coding Theory**, (Proceedings of a conference held at the USNA, Oct 1998), Springer-Verlag, 2000 book web page **Adventures with group theory: Rubik's cube, Merlin's machine, and other mathematical toys, 2nd ed.**, The Johns Hopkins Univer. Press, 2008. book web page- with Rick Kreminski and JoAnn Turisco,
**Applied Abstract Algebra**, The Johns Hopkins Univ Press, 2004. book web page - (co-editor)
**Advances in coding theory and cryptology**, (T. Shaska, W. C. Huffman, D. Joyner, V. Ustimenko, editors) Series on Coding Theory and Cryptology, 2. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007. x+267 pp. - with William Granville,
**Differential calculus and Sage**, Createspace, 2009. Available at amazon.com or free as a pdf, with latex source. Released under an open source cc-by-sa license. - with Jon-Lark Kim,
**Unsolved problems in coding theory**, Birkhäuser/Springer-Verlag, 2010. Available at amazon.com. - with Marshall Hampton,
**Introduction to Differential Equations Using Sage**, The Johns Hopkins University Press, September, 2012. - with Caroline Melles,
**Adventures in Graph Theory**, to appear in a Birkhauser series

A more frequently updated page of my papers and books can be found on the cv page.