Some properties of skew codes over finite fields

TL;DR

This paper explores algebraic and geometric properties of skew codes over finite fields, focusing on modules over skew polynomial rings, and establishes BCH-type bounds for their minimum distance when constructed with automorphisms.

Contribution

It introduces new algebraic and geometric insights into skew codes and provides BCH-type bounds for minimum distance in automorphism-based skew codes.

Findings

Analyzed algebraic properties of skew codes over finite fields.

Derived BCH-type lower bounds for minimum distance.

Focused on modules over skew polynomial rings with automorphisms.

Abstract

After recalling the definition of codes as modules over skew polynomial rings, whose multiplication is defined by using an automorphism and a derivation, and some basic facts about them, in the first part of this paper we study some of their main algebraic and geometric properties. Finally, for module skew codes constructed only with an automorphism, we give some BCH type lower bounds for their minimum distance.