Self-Dual Codes and Cyclic Codes over \(F_p + vF_p\)

Abstract

In this paper, we give a criterion to judge whether a linear code over the ring is self-dual. Moreover, we introduce the generating set in standard form for the cyclic codes over \(F_p + vF_p\), and characterize the structure of cyclic codes over the ring. Then we prove that cyclic codes over the ring are principally generated and obtain the unique generating idempotent for cyclic codes of length \(n\), where \(n\) is coprime to \(p\).