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The joint weight enumerators and Siegel modular forms
Author(s):
Y.
Choie;
M.
Oura
Journal:
Proc. Amer. Math. Soc.
134
(2006),
2711-2718.
MSC (2000):
Primary 94B05;
Secondary 11F46
Posted:
February 8, 2006
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Additional information
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:
-
- 1.
- Bannai, E., Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups, and reminiscences of Francois Jaeger (a survey). Symposium à la Memoire de Francois Jaeger (Grenoble, 1998). Ann. Inst. Fourier (Grenoble) 49 (1999), no. 3, 763-782. MR 1703422 (2001f:94011)
- 2.
- Choie, Y. and Sole, P., Ternary codes and Jacobi forms. Discrete Math. 282 (2004), no. 1-3, 81-87. MR 2059508 (2005a:11061)
- 3.
- Conway, J.H. and Sloane, N. J. A., Sphere Packings, Lattices and Groups (Second Edition), Springer-Verlag, NY, 1993. MR 1194619 (93h:11069)
- 4.
- Duke, W., On codes and Siegel modular forms, Internat. Math. Res. Notices, 1993, no. 5, 125-136. MR 1219862 (94d:11029)
- 5.
- Igusa, J., Theta functions, Die Grundlehren der mathematischen Wissenschaften, Band 194, Springer-Verlag, NewYork-Heidelberg, 1972. MR 0325625 (48:3972)
- 6.
- Igusa, J., On the ring of modular forms of degree two over
 , Amer. J. Math. 101 (1979), no. 1, 149-183. MR 0527830 (80d:10039) - 7.
- Lang, S., Introduction to modular forms, A series of Comprehensive Studies in Mathematics, Springer-Verlag (1976). MR 0429740 (55:2751)
- 8.
- S. Nagaoka, On the ring of Hilbert modular forms over
 , J. Math. Soc. Japan, Vol. 35, No. 4 (1983). MR 0714463 (84k:10020) - 9.
- Oura, M., Observation on the weight enumerators from classical invariant theory, preprint.
- 10.
- Ozeki, M., On basis problem for Siegel moduar forms of degree
 , Acta Arith., 31 (1976), no. 1, 17-30. MR 0432553 (55:5541) - 11.
- Pless, V. and Sloane, N. J. A., On the classification and enumeration of self-dual codes, J. Combinatorial Theory Ser.A 18 (1975), 313-335. MR 0376232 (51:12412)
- 12.
- Vardi, I., Coding theory (Multiple weight enumerators of codes), preprint 1998.
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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
DOI:
10.1090/S0002-9939-06-08263-3
PII:
S 0002-9939(06)08263-3
Keywords:
Code,
weight enumerator,
modular form
Received by editor(s):
November 1, 2004
Received by editor(s) in revised form:
March 14, 2005
Posted:
February 8, 2006
Communicated by:
Wen-Ching Winnie Li
Copyright of article:
Copyright
2006,
American Mathematical Society
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