Hermitian self-dual quasi-abelian codes

Year 2018, , 5 - 18, 15.01.2018

Herbert S. Palines Somphong Jitman Romar B. Dela Cruz

https://doi.org/10.13069/jacodesmath.327399

Cited By: 1

Abstract

Quasi-abelian codes constitute an important class of linear codes containing theoretically and practically interesting codes such as quasi-cyclic codes, abelian codes, and cyclic codes. In particular, the sub-class consisting of 1-generator quasi-abelian codes contains large families of good codes. Based on the well-known decomposition of quasi-abelian codes, the characterization and enumeration of Hermitian self-dual quasi-abelian codes are given. In the case of 1-generator quasi-abelian codes, we offer necessary and sufficient conditions for such codes to be Hermitian self-dual and give a formula for the number of these codes. In the case where the underlying groups are some $p$-groups, the actual number of resulting Hermitian self-dual quasi-abelian codes are determined.

Keywords

Hermitian self-dual codes, Quasi-abelian codes, 1-generator, p-groups

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