Several classes of minimal linear codes from weakly regular and non-weakly regular bent functions

Abstract

As a special subclass of linear codes, minimal linear codes have attracted considerable attention in coding theory and cryptography due to their significant applications in secret sharing schemes and secure two-party computation. In this paper, we are devoted to constructing minimal linear codes violating the Ashikhmin–Barg (AB for short) condition over finite fields of odd characteristic. First, we present several classes of minimal linear codes violating the AB condition from weakly regular bent functions and determine their weight distributions. Next, we construct four to six weights minimal linear codes violating the AB condition by using non-weakly regular bent functions. Meanwhile, their weight distributions are also provided. To the best of our knowledge, this paper is the first one to investigate the constructions of minimal linear codes that violate the AB condition by using both weakly regular and non-weakly regular bent functions over finite fields of odd characteristic.