New constructions of systematic authentication codes from three classes of cyclic codes

Abstract

Recently, several classes of cyclic codes with three nonzero weights were constructed. With the generic construction presented by C. Ding, T. Helleseth, T. Klove and X. Wang, we present new systematic authentication codes based on these cyclic codes. In this paper, we study three special classes of cyclic codes and their authentication codes. With the help of exponential sums, we calculate the maximum success probabilities of the impersonation and substitution attacks on the authentication codes. Our results show that these new authentication codes are better than some of the authentication codes in the literature. As a byproduct, the number of times that each element occurs as the coordinates in the codewords of the cyclic codes is settled, which is a difficult problem in general.