Generalized Quasi-Cyclic Codes Over \mathbbF_q+u\mathbbF_q

2013/07/06 by Gao, Jian, Fu, Fang-Wei, Shen, Linzhi
#11T71 #94B05 #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1307.1746

Abstract

Generalized quasi-cyclic (GQC) codes with arbitrary lengths over the ring \mathbbF_q+u\mathbbF_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, minimal generating sets and lower bounds on the minimum distance are given. As a special class of GQC codes, quasi-cyclic (QC) codes over \mathbbF_q+u\mathbbF_q are also discussed briefly in this paper.

Related

• Structure and Performance of Generalized Quasi-Cyclic Codes
• One generator quasi-cyclic codes over F2 + uF2 + vF2 + uvF2
• Skew Generalized Quasi-Cyclic Codes over Finite Fields
• On cyclic codes over ℤ_q+uℤ_q
• On Quasi-Cyclic Codes as a Generalization of Cyclic Codes