Four classes of minimal binary linear codes with $$w_{min}/w_{max}<1/2$$ derived from Boolean functions

Abstract

Due to wide applications in communications, data storage, and cryptography, linear codes have received much attention in the past decades. As a subclass of linear codes, minimal linear codes can be used to construct secret sharing schemes with nice access structure. This paper gives the weight distributions of four classes of minimal binary linear codes with $$w_{min}/w_{max}<1/2$$ derived from Boolean functions.