Abstract
Let F2m be a finite field of cardinality 2m, n be an odd positive integer, and denote R=F2m[u]∕〈u3〉. Let δ,α∈F2m×. Then (δ+αu2)-constacyclic codes over R are called constacyclic codes over R of Type 2. In this paper, an explicit representation and a complete description for all distinct (δ+αu2)-constacyclic codes over R of length 2n and their dual codes are given. Moreover, explicit formulas for the number of codewords in each code and the number of all such codes are provided respectively. In particular, all distinct self-dual (1+αu2)-constacyclic codes over R of length 2n are presented precisely. In addition, a complement to a result in Cao et al. (2017) is given.
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