Divisibility properties for covering radius of certain cyclic codes

We are presenting a new method to obtain the covering radius of codes and in particular to prove quasi-perfection in codes. Our techniques combine divisibility results of Ax-Katz and Moreno-Moreno as well as coding theoretic methods. We answer a problem posed by Cohen-Honkala-Litsyn-Lobstein in the book covering radius for Bose-Chaudhuri-Hocquenghem (BCH) codes. We also obtain the covering radius for many new classes of codes.