Title

Constacyclic Codes of Length p^s Over Fpm + uFpm

Publication Title

Journal of Algebra

Publication Date

9-2010

Document Type

Article

DOI

10.1016/J.JALGEBRA.2010.05.027

Keywords

cyclic codes, constacyclic codes, repeated-root codes, codes over rings, hamming distance

Disciplines

Algebra | Mathematics

Abstract

For any prime p, all constacyclic codes of length ps over the ring ℛ = Fpm + uFpm are considered. The units of the ring ℛ are of the forms γ and + , where , β, and γ are nonzero elements of Fpm, which provides pm (pm -1) such constacyclic codes. First, the structure and Hamming distances of all constacyclic codes of length ps over the finite field Fpm are obtained; they are used as a tool to establish the structure and Hamming distances of all ( + )-constacyclic codes of length ps over ℛ. We then classify all cyclic codes of length ps over ℛ and obtain the number of codewords in each of those cyclic codes. Finally, a one-to-one correspondence between cyclic and γ-constacyclic codes of length ps over ℛ is constructed via ring isomorphism, which carries over the results regarding cyclic codes corresponding to γ-constacyclic codes of length ps over ℛ.

Publisher

Elsevier

Publisher Location

Amsterdam, Netherlands


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