One task of coding theory is to determine the number of nonequivalent codes (or even give explicit constructions) with prescribed parameters, such as minimum weight, length, and dimension (for linear codes). In this paper, the author presents a construction of perfect q-ary codes by using the method he introduced in an earlier paper [1]. By counting the number of distinct codes obtained from this method, the author makes an improvement on the lower bound for the size of perfect q-ary codes with length n=(q^m-1)/(q-1).

Thus, the main contribution of this paper is the improvement on the lower bound of the size of perfect q-ary codes with the given length. Another interesting achievement, originally given in the author’s earlier paper [1], is the explicit construction of perfect q-ary codes, which may be developed and applied to other codes in the future.