Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902996 | Discrete Mathematics | 2018 | 13 Pages |
Abstract
Let R be the Galois ring GR(pk,s) of characteristic pk and cardinality psk. 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 rlm over R, where r,l, and t are three primes with 2â¤l, r|(qtâ1), lvâ¥(qtâ1) and gcd(rl,q(qâ1))=1. Finally, as applications, weight distributions of all irreducible cyclic codes for t=2 and generator polynomials of self-dual cyclic codes of length lm and rlm over R are given.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Yansheng Wu, Qin Yue, Fengwei Li,