Explicit representation for a class of Type 2 constacyclic codes over the ring F_2^m[u]/〈 u^2λ〉 with even length

05/08/2019

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by   Yuan Cao, et al.

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Let F_2^m be a finite field of cardinality 2^m, λ and k be integers satisfying λ,k≥ 2 and denote R=F_2^m[u]/〈 u^2λ〉. Let δ,α∈F_2^m^×. For any odd positive integer n, we give an explicit representation and enumeration for all distinct (δ+α u^2)-constacyclic codes over R of length 2^kn, and provide a clear formula to count the number of all these codes. As a corollary, we conclude that every (δ+α u^2)-constacyclic code over R of length 2^kn is an ideal generated by at most 2 polynomials in the residue class ring R[x]/〈 x^2^kn-(δ+α u^2)〉.