Describing A Cyclic Code by Another Cyclic Code

TL;DR

This paper introduces a novel method for bounding the minimum distance of q-ary cyclic codes by associating a second cyclic code, leading to improved bounds over existing methods like BCH and Hartmann–Tzeng.

Contribution

It presents a new approach that links two cyclic codes to derive tighter bounds on the minimum distance of the original code.

Findings

Improved bounds on minimum distance for several cyclic codes

Connection established between the new method and existing bounds

Demonstrated cases where the new bounds outperform traditional bounds

Abstract

A new approach to bound the minimum distance of $q$-ary cyclic codes is presented. The connection to the BCH and the Hartmann--Tzeng bound is formulated and it is shown that for several cases an improvement is achieved. We associate a second cyclic code to the original one and bound its minimum distance in terms of parameters of the associated code.