Affiliation of Author(s):理学院

Journal:DISCRETE MATHEMATICS

Key Words:Irreducible factorization Primitive idempotent Irreducible cyclic code

Abstract:Let F-q be a finite field of odd order q and n = 2(a)p(1)(a1)p(2)(a2), where a, a(1), a(2) are positive integers, p(1), P-2 are distinct odd primes and 4p(1)p(2)vertical bar q - 1. In this paper, we study the irreducible factorization of x(n) - 1 over F-q and all primitive idempotents in the ring F-q[x]/(x(n) - 1). Moreover, we obtain the dimensions and the minimum Hamming distances of all irreducible cyclic codes of length n over F-q. (C) 2016 Elsevier B.V. All rights reserved.

ISSN No.:0012-365X

Translation or Not:no

Date of Publication:2017-01-06

Co-author:Lifen

Correspondence Author:cxw