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

Authors : Seher TUTDERE

Pages : 20-26

Doi:10.15672/hujms.881649

View : 16 | Download : 10

Publication Date : 2022-02-14

Article Type : Research Paper

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