2020/01/07 by Qunying Liao, Yuanbo Liu, Liao, Qunying +1
Computer Science · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.2001.01897
arxiv created 2020/01/07 · openalex publication_date 2020/01/07 · arxiv updated 2020/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It's well known that the quadratic residue code over finite fields is an interesting class of cyclic codes for its higher minimum distance. Let g be a positive integer and p,p1,…, pg be distinct odd primes, the present paper generalizes the constructions for the quadratic residue code with length p to be the length n=p1⋯ pg, and to be the case m-th residue codes with length p over finite fields, where m≥ 2 is a positive integer. Furthermore, a criterion for that these codes are self-orthogonal or complementary dual is obtained, and then the corresponding counting formula are given. In particular, the minimum distance of all 24 quaternary quadratic residue codes [15,8] are determined.