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Affiliation of Author(s):理学院

Journal:DISCRETE MATHEMATICS

Key Words:Primitive idempotents Irreducible cyclic codes Weight distribution Self-dual cyclic codes

Abstract:Let R be the Galois ring GR(p(k), s) of characteristic p(k) and cardinality p(sk). Firstly, we give all primitive idempotent generators of irreducible cyclic codes of length n over R, and a p-adic integer ring with gcd(p, n) = 1. Secondly, we obtain all primitive idempotents of all irreducible cyclic codes of length rl(m) over R, where r, l, and t are three primes with 2 inverted iota 1, r vertical bar(q(t) - 1), l(v) vertical bar vertical bar (q(t) - t) and gcd(rl, q(q - 1)) = 1. Finally, as applications, weight distributions of all irreducible cyclic codes for t = 2 and generator polynomials of self-dual cyclic codes of length l(m) and rl(m) over R are given. (C) 2017 Elsevier B.V. All rights reserved.

ISSN No.:0012-365X

Translation or Not:no

Date of Publication:2018-06-01

Co-author:Wu, Yansheng,Li, Fengwei

Correspondence Author:yq