Residue codes of extremal Type II Z_4-codes and the moonshine vertex operator algebra

In this paper, we study the residue codes of extremal Type II Z_4-codes of length 24 and their relations to the famous moonshine vertex operator algebra. The main result is a complete classification of all residue codes of extremal Type II Z_4-codes of length 24. Some corresponding results associated to the moonshine vertex operator algebra are also discussed.Comment: 21 pages, shortened from v

Codes over F-4, Jacobi forms and Hilbert-Siegel modular forms over Q(A root 5)

We study codes over a finite field F-4. We relate self-dual codes over F-4 to real 5-mod ular lattices,nd to self-dual codes over F-2 via a Gray map. We construct Jacobi forms over Q(root 5) from the (omplete weight enumerators of self-dual codes over F-4. Furthermore, we relate Hilbert-Siegel forms to the joint weight enumerators of self-dual codes over F-4. (c) 2004 Elsevier Ltd. All rights reserved.X111sciescopu

Ozeki polynomials and Jacobi forms

A Jacobi polynomial was introduced by Ozeki. It corresponds to the codes over F-2. Later, Bannai and Ozeki showed how to construct Jacobi forms with various index using a Jacobi polynomial corresponding to the binary codes. It generalizes Broue-Enguehard map. In this paper, we study Jacobi polynomial which corresponds to the codes over F-2f. We show how to construct Jacobi forms with various index over the totally real field. This is one of extension of Broue-Enguehard map.X11sciescopu

Jacobi forms over totally real fields and type II codes over Galois rings GR(2(m), f)

In this paper, we study the invariant polynomial ring of the generalized Clifford-Weil group and give a connection to Jacobi modular forms over the totally real field. The invariant polynomials can be constructed from the weight enumerators of type II codes over the Galois rings. (C) 2003 Elsevier Ltd. All rights reserved.X119sciescopu

Invariant Ring of Clifford-Weil Group, Jacobi forms over Totally real fields

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On self-dual codes over some prime fields

AbstractIn this paper, we study self-dual codes over GF(p) where p=11,13,17,19,23 and 29. A classification of such codes for small lengths is given. The largest minimum weights of these codes are investigated. Many maximum distance separable self-dual codes are constructed