Explicit representation for a class of Type 2 constacyclic codes over the ring \mathbbF_2^m[u]/⟨ u^2λ⟩ with even length

2019/05/08 by Yuan Cao, Cao, Yuan, Yonglin Cao +7
Computer Science · #Coding theory and cryptography #Cellular Automata and Applications #Cryptography and Residue Arithmetic

paper · pdf · doi:10.48550/arxiv.1905.03621

Abstract

Let \mathbbF2m be a finite field of cardinality 2m, λ and k be integers satisfying λ,k≥ 2 and denote R=\mathbbF2m[u]/⟨ u2λ⟩. Let δ,α∈ \mathbbF2m×. For any odd positive integer n, we give an explicit representation and enumeration for all distinct (δ+αu2)-constacyclic codes over R of length 2kn, and provide a clear formula to count the number of all these codes. As a corollary, we conclude that every (δ+αu2)-constacyclic code over R of length 2kn is an ideal generated by at most 2 polynomials in the residue class ring R[x]/⟨ x2kn-(δ+αu2)⟩.

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