On the algebraic structure of quasi-cyclic codes of index 11/2

摘要

In this paper, we study quasi-cyclic codes of index and co-index 2m over Fq and their dual codes, where m is a positive integer, q is a power of an odd prime and gcd(m,q)=1. We characterize and determine the algebraic structure and the minimal generating set of quasi-cyclic codes of index and co-index 2m over Fq. We note that some optimal and good linear codes over Fq can be obtained from this class of codes. Furthermore, the algebraic structure of their dual codes is given.