论文信息 - Codes over F4, Jacobi forms and Hilbert-Siegel modular forms over Q(sqrt(5))

Codes over F4, Jacobi forms and Hilbert-Siegel modular forms over Q(sqrt(5))

We study codes over a finite field F4. We relate self-dual codes over F4 to real 5-modular lattices and to self-dual codes over F2 via a Gray map. We construct Jacobi forms over Q(√5) from the complete weight enumerators of self-dual codes over F4. Furthermore, we relate Hilbert-Siegel forms to the joint weight enumerators of self-dual codes over F4.

Koichi Betsumiya | YoungJu Choie

[1] W. Ebeling,et al. Lattices and Codes: A Course Partially Based on Lectures by F. Hirzebruch , 1994 .

[2] N. J. A. Sloane,et al. Self-Dual Codes over GF(4) , 1978, J. Comb. Theory, Ser. A.

[3] Patrick Solé,et al. Self-dual codes over Z~4 and half-integral weight modular forms , 2002 .

[4] Sophia Antipolis,et al. Type I1 Codes over F4 , 2002 .

[5] F. MacWilliams,et al. The Theory of Error-Correcting Codes , 1977 .

[6] Neil J. A. Sloane,et al. The theory of error-correcting codes (north-holland , 1977 .

[7] YoungJu Choie,et al. Jacobi forms over totally real fields and codes over ${\Bbb F}\sb p$ , 2002 .

[8] Masaaki Harada,et al. Type II Codes, Even Unimodular Lattices, and Invariant Rings , 1999, IEEE Trans. Inf. Theory.

[9] YoungJu Choie,et al. The complete weight enumerator of type II codes over Z2m and Jacobi forms , 2001, IEEE Trans. Inf. Theory.

[10] Bernhard Liehl,et al. On the group S L 2 over orders of arithmetic type. , 1981 .

[11] Patrick Solé,et al. Type II Codes Over F 4 + uF 4 . , 2001 .

[12] Howard Skogman. Jacobi forms over totally real number fields , 2001 .

[13] Wolfgang Ebeling,et al. Lattices and Codes: A Course Partially Based on Lectures by Friedrich Hirzebruch , 1994 .