Complete classification for simple root cyclic codes over local rings ℤ_p^s[v]/⟨ v²-pv⟩

2017/10/25 by Yuan Cao, Cao, Yuan, Yonglin Cao +1
Computer Science · #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · pdf · doi:10.48550/arxiv.1710.09236

openalex publication_date 2017/10/25 · openalex created_date 2017/11/10 · openalex updated_date 2026/07/28

Abstract

Let p be a prime integer, n,s≥ 2 be integers satisfying \rm gcd(p,n)=1, and denote R=ℤ_p^s[v]/⟨ v²-pv⟩. Then R is a local non-principal ideal ring of p^2s elements. First, the structure of any cyclic code over R of length n and a complete classification of all these codes are presented. Then the cardinality of each code and dual codes of these codes are given. Moreover, self-dual cyclic codes over R of length n are investigated. Finally, we list some optimal 2-quasi-cyclic self-dual linear codes over ℤ₄ of length 30 and extremal 4-quasi-cyclic self-dual binary linear [60,30,12] codes derived from cyclic codes over ℤ₄[v]/⟨ v²+2v⟩ of length 15.

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