Construction of a Class of Linear Codes with Two Weights

Abstract

In recent years, linear codes with few weights have been an interesting subject in both theory and practice, as these codes have applications in secret sharing schemes, data storage systems, association schemes and authentication codes. In this paper, we extend a special case of Li and Du et al. 's construction to a more general case. We construct a class of linear codes with two weights and determine the explicit weight distribution by exponential sums over finite fields. Finally, we demonstrate that the codes have essential applications in secret sharing schemes.