On constacyclic codes of length 4ps over Fpm + uFpm

For any odd prime p such that p(m) equivalent to 1 (mod 4), the structures of all lambda-constacyclic codes of length 4p(s) over the finite commutative chain ring F(p)m + uF(p)m (u(2) = 0) are established in terms of their generator polynomials. If the unit A is a square, each lambda-constacyclic code of length 4p(s) is expressed as a direct sum of an -alpha-constacyclic code and an alpha-constacyclic code of length 2p(s). In the main case that the unit lambda is not a square, it is shown that any nonzero polynomial of degree < 4 over F(p)m is invertible in the ambient ring (F(p)m+uF(p)m)[x]/(x(4ps)-lambda) When the unit lambda is of the form lambda = alpha + u beta for nonzero elements alpha, beta of F(p)m, it is obtained that the ambient ring (F(p)m+uF(p)m)[x]/x(4ps)-(alpha+u beta))is a chain ring with maximal ideal (x(4) - alpha(0)), and so the (alpha + u beta)-constacyclic codes are ((x(4) - alpha(0))(i)), for 0 <= i <= 2p(s). For the remaining case, that the unit lambda is not a square, and lambda = gamma for a nonzero element gamma of F(p)m, it is proven that the ambient ring F(p)m+uF(p)m)[x]/(x(4)ps-gamma) is a local ring with the unique maximal ideal (x(4) - gamma(0), u). Such lambda-constacyclic codes are then classified into 4 distinct types of ideals, and the detailed structures of ideals in each type are provided. Among other results, the number of codewords, and the dual of each lambda-constacyclic code are provided. (C) 2016 Elsevier B.V. All rights reserved.