The joint weight enumerators and Siegel modular forms
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- by Y. Choie and M. Oura PDF
- Proc. Amer. Math. Soc. 134 (2006), 2711-2718 Request permission
Abstract:
The weight enumerator of a binary doubly even self-dual code is an isobaric polynomial in the two generators of the ring of invariants of a certain group of order 192. The aim of this note is to study the ring of coefficients of that polynomial, both for standard and joint weight enumerators.References
- Eiichi Bannai, Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups, and reminiscences of François Jaeger (a survey), Ann. Inst. Fourier (Grenoble) 49 (1999), no. 3, 763–782 (English, with English and French summaries). Symposium à la Mémoire de François Jaeger (Grenoble, 1998). MR 1703422, DOI 10.5802/aif.1690
- YoungJu Choie and Patrick Solé, Ternary codes and Jacobi forms, Discrete Math. 282 (2004), no. 1-3, 81–87. MR 2059508, DOI 10.1016/j.disc.2003.12.002
- J. H. Conway and N. J. A. Sloane, Sphere packings, lattices and groups, 2nd ed., Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 290, Springer-Verlag, New York, 1993. With additional contributions by E. Bannai, R. E. Borcherds, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen and B. B. Venkov. MR 1194619, DOI 10.1007/978-1-4757-2249-9
- W. Duke, On codes and Siegel modular forms, Internat. Math. Res. Notices 5 (1993), 125–136. MR 1219862, DOI 10.1155/S1073792893000121
- Jun-ichi Igusa, Theta functions, Die Grundlehren der mathematischen Wissenschaften, Band 194, Springer-Verlag, New York-Heidelberg, 1972. MR 0325625, DOI 10.1007/978-3-642-65315-5
- Jun-ichi Igusa, On the ring of modular forms of degree two over $\textbf {Z}$, Amer. J. Math. 101 (1979), no. 1, 149–183. MR 527830, DOI 10.2307/2373943
- Serge Lang, Introduction to modular forms, Grundlehren der Mathematischen Wissenschaften, No. 222, Springer-Verlag, Berlin-New York, 1976. MR 0429740
- Sh\B{o}yū Nagaoka, On the ring of Hilbert modular forms over $\textbf {Z}$, J. Math. Soc. Japan 35 (1983), no. 4, 589–608. MR 714463, DOI 10.2969/jmsj/03540589
- Oura, M., Observation on the weight enumerators from classical invariant theory, preprint.
- Michio Ozeki, On basis problem for Siegel modular forms of degree 2, Acta Arith. 31 (1976), no. 1, 17–30. MR 432553, DOI 10.4064/aa-31-1-17-30
- Vera Pless and N. J. A. Sloane, On the classification and enumeration of self-dual codes, J. Combinatorial Theory Ser. A 18 (1975), 313–335. MR 376232, DOI 10.1016/0097-3165(75)90042-4
- Vardi, I., Coding theory (Multiple weight enumerators of codes), preprint 1998.
Additional Information
- Y. Choie
- Affiliation: Department of Mathematics, Pohang University of Science and Technology, Pohang, 790–784, Korea
- Email: yjc@postech.ac.kr
- M. Oura
- Affiliation: Department of Mathematics, Kochi University, Kochi, 780–8520, Japan
- Email: oura@math.kochi-u.ac.jp
- Received by editor(s): November 1, 2004
- Received by editor(s) in revised form: March 14, 2005
- Published electronically: February 8, 2006
- Communicated by: Wen-Ching Winnie Li
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 2711-2718
- MSC (2000): Primary 94B05; Secondary 11F46
- DOI: https://doi.org/10.1090/S0002-9939-06-08263-3
- MathSciNet review: 2213751