Ds-bounds for cyclic codes: new bounds for abelian codes

TL;DR

This paper introduces a method to extend bounds from cyclic codes to abelian codes, enabling improved bounds for multivariate codes and advancing the understanding of their structure.

Contribution

The paper presents a novel technique to generalize ds-bounds from cyclic to abelian codes, enhancing the search for tighter bounds.

Findings

Extended cyclic code bounds to abelian codes

Improved bounds for abelian codes

Enhanced methods for code analysis

Abstract

In this paper we develop a technique to extend any bound for cyclic codes constructed from its defining sets (ds-bounds) to abelian (or multivariate) codes. We use this technique to improve the searching of new bounds for abelian codes.