A class of repeated-root constacyclic codes over F<inf>p^m</inf>[u]/〈u^e〉 of Type 2

Abstract

© 2018 Elsevier Inc. Let Fpm be a finite field of cardinality pm where p is an odd prime, n be a positive integer satisfying gcd(n,p)=1, and denote R=Fpm[u]/〈ue〉 where e≥4 be an even integer. Let δ,α∈Fpm×. Then the class of (δ+αu2)-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 (δ+αu2)-constacyclic codes over R of length npk 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 (δ+αu2)-constacyclic codes over Fpm[u]/〈ue〉 of length pk and their dual codes are presented precisely.