Some Results on Generalized Quasi-Cyclic Codes over $\mathbb{F}_q+u\mathbb{F}_q$

Jian GAO; Fang-Wei FU; Linzhi SHEN; Wenli REN

doi:10.1587/transfun.E97.A.1005

Regular Section

Some Results on Generalized Quasi-Cyclic Codes over $\mathbb{F}_q+u\mathbb{F}_q$

Jian GAO, Fang-Wei FU, Linzhi SHEN, Wenli REN

Author information

Keywords: generalized quasi-cyclic codes, 1-generator generalized quasi-cyclic codes, minimum generating sets, minimum distances

JOURNAL RESTRICTED ACCESS

2014 Volume E97.A Issue 4 Pages 1005-1011

DOI https://doi.org/10.1587/transfun.E97.A.1005

Details

Abstract

Generalized quasi-cyclic (GQC) codes with arbitrary lengths over the ring $\mathbb{F}_{q}+u\mathbb{F}_{q}$, where u²=0, q=pⁿ, n a positive integer and p a prime number, are investigated. By the Chinese Remainder Theorem, structural properties and the decomposition of GQC codes are given. For 1-generator GQC codes, minimum generating sets and lower bounds on the minimum distance are given.

Corresponding author

Register with J-STAGE for free!