On Upper Bounds for Minimum Distances and Covering Radius of Non-binary Codes

We consider upper bounds on two fundamental parameters of a code; minimum distance and covering radius. New upper bounds on the covering radius of non-binary linear codes are derived by generalizing a method due to S. Litsyn and A. Tiett avv ainen 10] and combining it with a new upper bound on the asymptotic information rate of non-binary codes. The new upper bound on the information rate is an application of a shortening method of a code. These results improve on the best presently known asymptotic upper bounds on minimum distance and covering radius of non-binary codes in certain intervals.