A class of repeated-root constacyclic codes over F_(p~m)[u]/ of Type 2

摘要

Let F-pm be a finite field of cardinality p(m) where p is an odd prime, n be a positive integer satisfying gcd(n,p) = 1, and denote R = F-pm [u]/ u(e) where e = 4 be an even integer. Let delta, alpha is an element of F-pm(x). Then the class of (delta + alpha u(2))-constacyclic codes over R is a significant subclass of constacyclic codes over R of Type 2. For any integer k = 1, an explicit representation and a complete description for all distinct (delta + alpha u(2))-constacyclic codes over R of length np(k) and their dual codes are given. Moreover, formulas for the number of codewords in each code and the number of all such codes are provided respectively. In particular, all distinct (delta + alpha u(2))-constacyclic codes over F-pm [u]/ u(e) of length p(k) and their dual codes are presented precisely. (C) 2018 Elsevier Inc. All rights reserved.