2023/11/29 by Ou-azzou, Hassan, Najmeddine, Mustapha, Aydin, Nuh
#11-XX #94Bxx #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2311.17527
In this paper we generalize the notion of n-equivalence relation introduced by Chen et al. in \citeChen2014 to classify constacyclic codes of length n over a finite field \mathbbFq, where q=pr is a prime power, to the case of skew constacyclic codes without derivation. We call this relation (n,σ)-equivalence relation, where n is the length of the code and σ is an automorphism of the finite field. We compute the number of (n,σ)-equivalence classes, and we give conditions on λ and μ for which (σ, λ)-constacyclic codes and (σ, λ)-constacyclic codes are equivalent with respect to our (n,σ)-equivalence relation. Under some conditions on n and q we prove that skew constacyclic codes are equivalent to cyclic codes. We also prove that when q is even and σ is the Frobenius autmorphism, skew constacyclic codes of length n are equivalent to cyclic codes when gcd(n,r)=1. Finally we give some examples as applications of the theory developed here.