Constacyclic codes of length ps over Fpm + uFpm

JOURNAL OF ALGEBRA

卷:324

Article

Dinh, Hai Q.

关键词: Cyclic codes;    Constacyclic codes;    Repeated-root codes;    Codes over rings;    Hamming distance;   

DOI  :  10.1016/j.jalgebra.2010.05.027

来源: Elsevier

【 摘 要 】

For any prime p, all constacyclic codes of length p(s) over the ring R = F-pm + uF(p)m are considered. The units of the ring R are of the forms gamma and alpha + u beta, where alpha, beta, and gamma are nonzero elements of F-pm. which provides pm(pm 1) such constacyclic codes. First, the structure and Hamming distances of all constacyclic codes of length p(s) over the finite field F-pm are obtained: they are used as a tool to establish the structure and Hamming distances of all (alpha + u beta)-constacyclic codes of length p(s) over R. We then classify all cyclic codes of length p(s) over R and obtain the number of codewords in each of those cyclic codes. Finally, a one-to-one correspondence between cyclic and gamma-constacyclic codes of length 195 over R is constructed via ring isomorphism, which carries over the results regarding cyclic codes corresponding to gamma-constacyclic codes of length p(s) over R. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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