On a class of constacyclic codes of length 2p^sover(Formula presented)

Abstract

©2018 Korean Mathematial Soiety. The aim of this paper is to study the class of Λ-constacyclic codes of length 2psover the finite commutative chain ring Ra=(Formula presented) = Fpm+ uFpm+ · · · + ua−1Fpm, for all units Λ of Rathat have the form Λ = Λ0+ uΛ1+ · · · + ua−1Λa−1, where Λ0, Λ1,…, Λa−1∈ Fpm, Λ0≠ 0, Λ1≠ 0. The algebraic structure of all Λ-constacyclic codes of length 2psover Raand their duals are established. As an application, this structure is used to determine the Rosenbloom-Tsfasman (RT) distance and weight distributions of all such codes. Among such constacyclic codes, the unique MDS code with respect to the RT distance is obtained.