Constructions of quantum BCH codes based on finite fields of odd characteristic

Let F_q be finite field with q elements, where q is a power of an odd prime p. Sufficient and necessary conditions for the self orthogonality of two classes of classical q-ary non-primitive BCH codes over F_q of length n = q^m -1 and n = q^r-1/q^m-1 are given, respectively. These conditions allow us to derive the parameters of four series of g-ary quantum BCH codes as a function of their design parameters based on some construction methods.