Linear codes with few weights from cyclotomic classes and weakly regular bent functions

Abstract

Linear codes with few weights constructed from defining sets have been extensively studied due to their applications in data storage systems, secret sharing schemes and authentication codes. In this paper, inspired by the works of Li et al. (Appl Algebra Eng Commun Comput 28(1):11–30, 2017) and Jian et al. (Finite Fields Appl 57:92–107, 2019), we propose a class of five-weight linear codes by choosing the defining set from cyclotomic classes, which includes a class of two-weight linear codes as a special case, and we also present two classes of two or three-weight linear codes by employing weakly regular bent functions. Besides, we obtain a class of two-weight optimal punctured codes with respect to the Griesmer bound.