A Novel Application of Boolean Functions With High Algebraic Immunity in Minimal Codes

Boolean functions with high algebraic immunity are important cryptographic primitives in some stream ciphers. In this paper, two methodologies for constructing minimal binary codes from sets, and vectorial immunity, proposed. More precisely, a general construction of new using contained Reed-Muller sets without nonzero low degree annihilators is presented. The other allows us to yield certain subcodes immunity. Via these constructions, infinite families linear dimension m length less than or equal m(m+1)/2 obtained. Besides, lower bound on the minimum distance proposed established. Conjectures open problems also results paper show that have nice applications several fields additionally symmetric cryptography, such as coding theory secret sharing schemes.