On the covering radii of a class of binary primitive cyclic codes

Year 2022, Volume: 51 Issue: 1, 20 - 26, 14.02.2022

Seher Tutdere

https://doi.org/10.15672/hujms.881649

Cited By: 1

Abstract

 In 2019, Kavut and Tutdere proved that the covering radii of a class of primitive binary cyclic codes with minimum distance greater than or equal to $r+2$ is $r$, where $r$ is an odd integer, under some assumptions. We here show that the covering radii $R$ of a class of primitive binary cyclic codes with minimum distance strictly greater than $\ell$ satisfy $r\leq R \leq \ell$, where $\ell,r$ are some integers, with $\ell$ being odd, depending on the given code. This new class of cyclic codes covers that of Kavut and Tutdere. 

Keywords

cyclic code, covering radius, finite field, polynomial equations

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