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

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 l satisfy r < R < l, where l, r are some integers, with l being odd, depending on the given code. This new class of cyclic codes covers that of Kavut and Tutdere.