Multi-dimensional Constacyclic Codes of Arbitrary Length over Finite Fields

2022/01/04 by Swati Bhardwaj, Bhardwaj, Swati, Madhu Raka +1
Computer Science · Social Sciences · #Coding theory and cryptography #Cooperative Communication and Network Coding #Islamic Finance and Communication

paper · pdf · doi:10.48550/arxiv.2201.01031

Abstract

Multi-dimensional cyclic code is a natural generalization of cyclic code. In an earlier paper we explored two-dimensional constacyclic codes over finite fields. Following the same technique, here we characterize the algebraic structure of multi-dimensional constacyclic codes, in particular three-dimensional (α,β,γ)- constacyclic codes of arbitrary length sℓ k and their duals over a finite field \mathbbF_q, where α,β,γ are non zero elements of \mathbbF_q. We give necessary and sufficient conditions for a three-dimensional (α,β,γ)- constacyclic code to be self-dual.

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