In 2003, Moreno and Castro proved that the covering radius of a class of primitive cyclic codes over the finite field F_2 having minimum distance 5 (resp. 7) is 3 (resp. 5). In this talk we give a generalization of this result as follows: the covering radius of a class of primitive cyclic codes over F_2 with minimum distance greater than or equal to r+2 is r, where r is any odd integer. Moreover, we discuss the covering radiii of the primitive binary e-error correcting BCH codes of length 2^f − 1. This is a joint work with Sel¸cuk Kavut.