|
Self-dual codes over  and half-integral weight modular forms
Author(s):
YoungJu
Choie;
Patrick
Solé
Journal:
Proc. Amer. Math. Soc.
130
(2002),
3125-3131.
MSC (1991):
Primary 05E20, 11F11, 11F50, 94B99, 05E99
Posted:
May 22, 2002
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper, we find a connection between the weight enumerator of self-dual  codes and half-integral weight modular forms. We generalize in that way results of Broué-Enguehard, Hirzebruch, Ozeki, Rains-Sloane, Runge.
References:
-
- 1.
- E. Bannai, M. Ozeki, Construction of Jacobi forms from certain combinatorial polynomials, Proceedings of the Japan Ac., Vol. 72, Ser. A, No 1 (1996) 12-15. MR 98a:11060
- 2.
- M. Broué, M. Enguehard, Polynômes des poids de certains codes et fonctions theta de certains réseaux, Ann. Sc. ENS 5 (1972) 157-181. MR 48:3596
- 3.
- A. Bonnecaze, P. Solé, A.R.C. Calderbank, Quaternary Constructions of Unimodular Lattices, IEEE Trans. on Information Theory, IT-41 (1995) 366-377. MR 96b:94027
- 4.
- Y. Choie and H. Kim, Codes over
 and Jacobi forms of genus  , Journal of Combinatorial Theory-Series A 95 (2001) 335-348. - 5.
- Y. Choie and N. Kim, The complete weight enumerator of Type II codes over
 and Jacobi Forms, IEEE Transactions on Information Theory, Vol. IT-47, pp.396-399 (2001). MR 2001m:11072 - 6.
- J.H. Conway, N.J.A. Sloane, Sphere Packings, Lattices and Groups Springer (1998) 3rd edition. MR 2000b:11077
- 7.
- W. Duke, Codes and Siegel Modular Forms, International Research Notices in Math., 3, p.125 in Duke Math. J. 70 (1993). MR 94d:11029
- 8.
- W. Ebeling, Lattices and Codes, Vieweg (1994). MR 95c:11084
- 9.
- M. Eichler, D. Zagier, The theory of Jacobi forms, Birkhäuser (1985). MR 86j:11043
- 10.
- A. M. Gleason, Weight enumerators of self-dual codes and MacWilliams identities, Actes du Congrés International de mathématiques, vol. 3, Gauthier-Villars (1970) 211-215. MR 54:12354
- 11.
- F. Klein, Vorlesungen uber das Ikosaeder und die Auflosung der Gleichungen vom funften Grade. (German) [Lectures on the icosahedron and the solution of equations of fifth degree] Reprint of the 1884 original. Edited, with an introduction and commentary by Peter Slodowy. Birkhauser Verlag, Basel; B. G. Teubner, Stuttgart, (1993). MR 96g:01046
- 12.
- F.J. MacWilliams, N.J.A. Sloane, The theory of Error Correcting Codes, North-Holland second edition (1981). MR 57:5408a; MR 57:5408b (review of original volumes)
- 13.
- M. Ozeki, On the notion of Jacobi polynomials for codes, Math. Proc. Cambridge Phil. Soc. (1997). MR 98b:11126
- 14.
- E.M. Rains, N.J.A. Sloane, Self-dual codes, in The Handbook of Coding Theory I, V.S. Pless and W.C. Huffman, eds., North-Holland (1998). MR 2000h:94001
- 15.
- B. Runge, On Siegel Modular forms I, Crelle 436 (1993) 57-85. MR 94c:11041
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
05E20, 11F11, 11F50, 94B99, 05E99
Retrieve articles in all Journals with MSC
(1991):
05E20, 11F11, 11F50, 94B99, 05E99
Additional Information:
YoungJu
Choie
Affiliation:
Department of Mathematics, Pohang University of Science and Technology, Pohang, 790--784, Korea
Email:
yjc@postech.ac.kr
Patrick
Solé
Affiliation:
CNRS-I3S, ESSI, Route des Colles, 06 903 Sophia Antipolis, France
Email:
ps@essi.fr
DOI:
10.1090/S0002-9939-02-06648-0
PII:
S 0002-9939(02)06648-0
Received by editor(s):
August 5, 2000
Posted:
May 22, 2002
Additional Notes:
This research was partially supported by COM2MAC
Communicated by:
Dennis A. Hejhal
Copyright of article:
Copyright
2002,
American Mathematical Society
|
Comments: webmaster@ams.org