MDS Triple skew cyclic codes

Rachid Mammeri1, Nabil Bennenni1, Aicha Batoul1
1Algebra and Number Theory Laboratory, Department of Algebra and Number Theory, Faculty of Mathematics, University of Science and Technology Houari Boumediene, BP 32, El Alia, 16111 Bab Ezzouar, Algiers, Algeria

Abstract

The present paper gives a detailed study of the structural theory of triple \(\theta\)-skew cyclic codes where the codes are over \(\mathbb{F}_q\). We give a complete characterization of these codes, focusing on their representation as modules. We identify the generator polynomials for the triple skew-cyclic codes as well as those of their duals. We explore the properties of these generator polynomials and their relationship to the code’s structure. Additionally,To illustrate our approach, we give concrete instances of triple \(\theta\)-skew cyclic codes to demonstrate how these structures can behave in practice. The special instances we present reveal that such codes are capable of achieving strong parameters under certain conditions.

Keywords: skew cyclic code, triple \(\theta\)-skew cyclic code, dual computational results