Good reversible quasi-cyclic codes via unfolding cyclic codes

Abstract

In this paper, we consider the reversibility problem in the class of quasi-cyclic (QC) codes Q over F_q of length nℓ and index ℓ generated by unfolding cyclic codes C over F_qℓ of length n. We prove a necessary and sufficient condition on C that ensures the reversibility of Q. Using computer search, we offer some good reversible QC codes that are generated by unfolding cyclic codes.