  In this paper we study the family of cyclic codes such that its minimum
distance reaches the maximum of its BCH bounds. We also show a way to construct
cyclic codes with that property by means of computations of some divisors of a
polynomial of the form X^n-1. We apply our results to the study of those BCH
codes C, with designed distance delta, that have minimum distance d(C)= delta.
Finally, we present some examples of new binary BCH codes satisfying that
condition. To do this, we make use of two related tools: the discrete Fourier
transform and the notion of apparent distance of a code, originally defined for
multivariate abelian codes.
