Equivalence between the BCH Bound and the Schaub Bound for Cyclic Codes

The Schaub bound is one of well-known lower bounds of the minimum distance for given cyclic code C, and defined as the minimum value, which is a lower bound on rank of matrix corresponding a codeword, in defining the set for all cyclic sub-codes of a given code C. In this paper, we show equivalence between the Schaub* bound defined by F. Ponchio and M. Sala, and the BCH bound for a cyclic code C. Moreover in order to compute the Schaub* bound, we give an important property of a lower bound on rank of a generic matrix for a cyclic code