ON THE TRUE MINIMUM DISTANCE OF HERMITIAN CODES

Abstract

A class of geometric Goppa codes based on Hermitian curves was introduced by Stichtenoth [3]. These codes are parametrized by an integer m that governs both dimension and minimum distance of the code. In that paper, the exact minimum distance is given in the range that 0 less-than-or-equal-to m less-than-or-equal-to q3 - q2 or m = 0 (mod q) with m < q3. In this paper we determine the exact minimum distance of these codes for any m with m greater-than-or-equal-to q3 - q2. Taken together the two results give the exact minimum distance of Hermitian codes for all values of the parameter m.