Weight distributions of two classes of linear codes with five or six weights

Abstract

Linear codes with few weights have been an interesting subject of study for many years, as these codes have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, two classes of five-weight or six-weight linear codes over Fp are constructed and their weight distributions are determined by means of exponential sums. In one case, there are some almost optimal codes with respect to the Griesmer bound, which are in fact optimal according to the online code tables.