The covering radii of a class of binary cyclic codes and some BCH codes

Abstract

In 2003, Moreno and Castro proved that the covering radius of a class of primitive cyclic codes over the finite field $$\mathbb {F}_2$$ having minimum distance 5 (resp. 7) is 3 (resp. 5). We here give a generalization of this result as follows: the covering radius of a class of primitive cyclic codes over $$\mathbb {F}_2$$ with minimum distance greater than or equal to $$r+2$$ is r, where r is any odd integer. Moreover, we prove that the primitive binary e-error correcting BCH codes of length $$2^f-1$$ have covering radii $$2e-1$$ for an improved lower bound of f.