W. David Joyner

Research Interests: graph theory, error-correcting codes, representation theory and applications, harmonic analysis on groups, applications of number theory/group theory to communication theory and cryptography, analytic number theory.
Ph.D.: University of Maryland-College Park, 1983-05-23

Other interests: Writing, chess, photography, video, history of mathematics and history of cryptography.

Brief Research Biography


  • University of Maryland, College Park (Ph.D. in Mathematics, May 1983; advisor: John Benedetto)
  • Georgia Institute of Technology, Atlanta (B.S. in Applied Mathematics, June 1981)


  • U. S. Naval Academy, Annapolis, MD (8/1987 – present)
  • Institute for Advanced Study, Princeton N.J. (Member, 4/1985 – 7/1987, NSF Fellow)
  • Princeton University (Instructor, 9/1985-6/1986, NSF Fellow)
  • University of California at San Diego, La Jolla, Ca. (Assist. Prof., 7/1984-3/1985, NSF Fellow)
  • University of Maryland, College Park (Research Instructor and Graduate Teaching Assistant, 9/1983-5/1984)
  • Georgia Institute of Technology, Atlanta (Undergraduate Teaching Assistant and Graduate Teaching Assistant, 9/1979-8/1981)

USNA Faculty Researcher of the Year Award, 2007.


  • Technical editor for Cryptologia 1999-2000, and now am on its editorial board.
  • Edited or co-edited three books (see below).
  • Some refereeing for various professional journals.


  • Contributed code and documentation to Sagemath and SymPy. I also help maintain the Sagemath email lists (for teaching, support, and development, resp.).
  • From 2000-2009, I was the maintainer of the GUAVA package, a package for GAP containing many routines for exploring error-correcting codes. Curently the maintainer is Joe Fields.
  • Creator and current maintainer of the TORIC package for computing with toric varieties.

Research Publications:

  1. “Zeta functions and their associated operators,” unpublished paper from 1981
  2. “A note on gaps between zeroes of L-functions,” unpublished paper dating from 1984.
  3. “Summation operators and ‘explicit formulas'”, Port. Math. 44(1987)119-130. (paper – basically my PhD thesis)
  4. “On the metaplectic analog of Kazhdan’s ‘endoscopic’ lifting”, Isr. J. Math. 61 (1988)113-154. (paper)
  5. “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
  6. “On twisted orbital integral identities for PGL(3) over a p-adic field”, Can. J. Math. 31(1991)1098-1130. paper
  7. “On the Montgomery-Dyson hypothesis”, in Proceedings of the Amalfi Analytic Number Theory Conference, Univ. de Salerno, 1992. paper
  8. “Remarks on the Bruggeman-Kutznetsov formula”, Proceedings of the Amalfi Analytic Number Theory Conference, Univ. de Salerno, 1992.
  9. “Simple local trace formulas for unramified p-adic groups”, Pac. J. Math.154(1992)103-129.
    paper (pdf)
  10. with Roland Martin, “Decomposing Lie Algebra Representations Using Crystal Graphs”, SAC Newsletter, no. 2, June 1997, pp. 27-34. paper
  11. with R. Martin, “Using crystal graphs to decompose Lie algebra representations”, SIGSAM Bull. 31 Dec. 1997.
  12. with R. Martin, “Branching rules for Lie algebra representations using crystal graphs”, Maple Tech. 25(1998)23-27. paper
  13. “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
  14. 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
  15. “On the unitary dual of the metaplectic cover of SL(2,F), for F p-adic,” unpublished paper, 1999.
  16. “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
  17. “On finite dimensional representations of non-connected reductive groups,” J. of Lie Theory 10(2000)269-284. On the JLT web page
  18. “Invariant distributions on the n-fold metaplectic covers of GL(r,F), F p-adic,” J. Fourier Anal. and Appl. 7(2001)343-358.
  19. 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
  20. 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. paper
  21. with Michael Fourte, “Odd King Tours on Even Chessboards,” Journal of Recreational Mathematics 31(2003)173-177.
  22. “Arithmetic of characters of generalized symmetric groups,” Archiv der Mathematik, vol 81 (2003)113–120.
  23. with Helena Verrill, “Notes on toric varieties,” preprint at math arxivs. “Computing with toric varieties,” J. Symb. Comp. Volume 42 (2007)511-532 .
  24. “Toric codes over finite fields”, AAECC, vol. 15, Number 1 (2004)63 – 79. A version may be found at math arXivs
  25. with Will Traves, “Representations of finite groups on Riemann-Roch spaces,” available at math arXivs.
  26. 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.
  27. 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. )
  28. (with Amy Ksir) “Automorphism groups of some AG codes” IEEE Trans. Info. Theory, vol 52, July 2006, pp 3325-3329.
    IEEE versionmath arXiv version.
  29. “Open Source Computer Algebra Systems – Maxima”, ACM Communications in Computer Algebra, Volume 40, Number 3/4 – September/December 2006 – Issue 157/158.
  30. 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.)
  31. 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 Ukrainian, and as a pdf file.
  32. “Conjectural permutation decoding of some AG codes” Communications in Computer Algebra (formerly “SIGSAM Bull”), vol 39, March 2005, pages 166-172.
  33. (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.)
  34. (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.
  35. (with William Stein) “SAGE: System for Algebra and Geometry Experimentation”, Communications in Computer Algebravol 39, June 2005, pages 61-64.
  36. “GUAVA: An error-correcting codes package” Communications in Computer Algebra, vol 39, June 2005, pages 65-68.
  37. “Mathematics of Ghaly’s machine”, Integers.
  38. “Quadratic residue codes and hyperelliptic curves”Discrete Mathematics and Theoretical Computer Science, vol 10(2008) 129-146.
  39. “Open Source Computer Algebra Systems – Axiom”, ACM Communications in Computer Algebra, Volume Volume 42, Number 2 – June 2008 – Issue 164.
  40. (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.
  41. (with Amy Ksir, Roger Vogeler) “Group representations on Riemann-Roch spaces of some Hurwitz curves” Albanian Journal of MathematicsVolume 1, Number 2 (2007)67-85 (electronic version). math arXivs.
  42. “A primer on computational group homology and cohomology.” . Proceedings of the Gaglione conference, entitled Aspects of Infinite Groups (ed. Ben Fine, G. Rosenberger, D. Spellman), World Scientific Press, 2008.
  43. (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 the pdf.)
  44. with Amy Ksir and Darren Glass, “Codes from Riemann-Roch spaces for y2 = xp-x over GF(p)”, Algebraic and Combinatorial Coding Theory in Honour of the Retirement of Vera Pless, a special issue ofInternational. J. of Information and Coding Theory, (editors: Philippe Gaborit, Jon-Lark Kim, Patrick Sole, and Isaac Woungang), 2010. pdf
  45. with Amy Ksir and Caroline Melles, “Automorphism Groups on Tropical Curves: Some Cohomology Calculations.” Beitrage zur Algebra und Geometrie, Volume 53, Issue 1 (2012)41-56.
  46. with Chris Christensen and Jenna Torres, “Lester Hill’s error-detecting codes”, Cryptologia, 36(2011)88-103.
  47. with Ondrej Certik, Aaron Meurer, Brian Granger, “Open Source Computer Algebra Systems: SymPy” to appear in ACM Communications in Computer Algebra, (2012, December). Available: pdf
  48. with Charles Celerier, David Joyner, Caroline Melles, David Phillips, “On the Walsh-Hadamard transform of monotone Boolean functions” in Tbilisi Mathematical Journal Special Issue on Sage and Research, vol 5(2012)19-35
  49. “Zeros of Some Self-Reciprocal Polynomials”, in Excursions in Harmonic Analysis: The February Fourier Talks at the Norbert Wiener Center (Applied and Numerical Harmonic Analysis series), ed. Travis D Andrews, Radu Balan, John J. Benedetto, Wojciech Czaja, Kasso A. Okoudjou, Birkhäuser, Boston, 2013. Available: paper.
  50. book review: “Review of Algebraic Shift Register Sequences by Mark Goresky and Andrew Klapper” in Cryptologia, Vol. 37(2013)175-183.
  51. book review: “Review of Cryptographic Boolean Functions and Applications by Thomas Cusick and Pantelimon Stănică” in Cryptologia, Vol. 37(2013)189-192.
  52. “A note on cryptologic aspects of the Waberski trial”, 7 pages, 2013. pdf
  53. “Elizebeth Smith Friedman, up to 1934”, 20 pages, 2013. pdf
  54. with Charles Celerier, Caroline Melles, David Phillips, Steven Walsh, “Explorations of edge-weighted Cayley graphs and p-ary bent functions”, arxiv link.
    A shorter version was published in INTEGERS, vol. 16 (2016)
  55. The Man Who Discovered God’s Number, College Math Journal, Sep. 2014 (
  56. with T. Shaska, “Self-inversive polynomials, curves, and codes”, pdf, Contemporary Math. American Math. Society, (to appear).
  57. “Hill vs Hamming” (expository), 2016. See also this blog post and this article.
  58. (with Alfred J. Menezes, Paul C. van Oorschot, Tony Shaska), Coding theory, coding theory chapter for the new edition of CRC Handbook of Discrete and Combinatorial Mathematics, to appear.
  59. “An Application of Matrix Theory to Baseball Rankings”, Mathematica Militaris, 22(2017)29-39.


  1. Distribution theorems of L-functions, Pitman Research Notes, vol 142, Longman Scientific and Technical, 1986. See also errata
  2. with G. Nakos, Linear algebra and its applications, Brooks-Cole (ITP), 1998.
  3. (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
  4. 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, errata page
  5. with Rick Kreminski and JoAnn Turisco, Applied Abstract Algebra, The Johns Hopkins Univ Press, 2004. book web page
  6. (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.
  7. with William Granville, Differential calculus and Sage, Createspace, 2009. Available at or free as a pdf, with latex source. Released under an open source cc-by-sa license.
  8. with Jon-Lark Kim, Selected unsolved problems in coding theory, Birkhäuser/Springer-Verlag, 2011. Available at
  9. with Marshall Hampton, Differential equations with Sage, Johns Hopkins University Press, 2012.
  10. with Caroline Melles, Adventures in Graph Theory, submitted, Birkhauser.
  11. with David Phillips, Graph theory and Algorithms and Optimization book, in preparation.


  1. Screencast on Love, War and Zombies – Systems of Differential Equations using Sage, with slides.
  2. Lanchester’s equations video
  3. The Bifid and Vigenere ciphers and Sage screencast
  4. Fourier series – using Sage video


David Joyner
572C Holloway Rd
Mathematics Dept
US Naval Academy
Annapolis, MD 21402