Repeated-root constacyclic codes of length 2p~s over Fpm +uFpm +u~2Fpm

摘要

Let lambda be a unit of the finite commutative chain ring R = F-pm + uF(pm) + u(2)F(pm) = {alpha+ u beta + u(2)gamma : alpha, beta, gamma is an element of F-pm} with u(3) = 0, where p is an odd prime and m is a positive integer. In this paper, we consider any lambda-constacyclic codes of length 2p(s) over R. In the case of square lambda = delta(2), where delta is an element of R, the algebraic structures of all lambda-constacyclic codes of length 2p(s) over R are determined by the Chinese Remainder Theorem in terms of polynomial generators. Precisely, each lambda-constacyclic code of length 2p(s) is represented as a direct sum of a (-delta)-constacyclic code and a delta-constacyclic code of length p(s). In the case of non-square lambda = alpha + u beta + u(2)gamma or lambda = alpha + u beta, where alpha, beta, gamma is an element of F-pm {0}, it is shown that the ring R = R[x]/ x(2ps) -lambda is a chain ring. In the case of non-square lambda = alpha is an element of F-pm {0}, it turns out that lambda-constacyclic codes are classified into 8 distinct types of ideals, and the detailed structures of ideals in each type are provided.