Bounds and Equivalence of Skew Polycyclic Codes over Finite Fields

2025/07/23 by Hassan Ou-azzou, Anna-Lena Horlemann, Ou-azzou, Hassan +3 · 2 citations
Computer Science · Mathematics · #Coding theory and cryptography #Cryptography and Residue Arithmetic #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2507.17571

Abstract

We study skew polycyclic codes over a finite field \mathbbF_q, associated with a skew polynomial f(x) ∈ \mathbbF_q[x;σ], where σ is an automorphism of \mathbbF_q. We start by proving the Roos-like bound for both the Hamming and the rank metric for this class of codes. Next, we focus on the Hamming and rank equivalence between two classes of polycyclic codes by introducing an equivalence relation and describing its equivalence classes. Finally, we present examples that illustrate applications of the theory developed in this paper.

Cited by

• Using nonassociative algebras to classify skew polycyclic codes up to isometry and equivalence
• When isometry and equivalence for skew constacyclic codes coincide

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• Skew Generalized Polycyclic Codes with Derivations
• Some properties of skew codes over finite fields
• On (n,σ)-equivalence relation between skew constacyclic codes
• Equivalence of Families of Polycyclic Codes over Finite Fields
• A note on the duals of skew constacyclic codes