Ideal access structures based on a class of minimal linear codes

Abstract

Coding theory is one of ways to construct ideal access structures. However, in general, determining the ideal access structures of the secret sharing schemes based on linear codes is very hard. According to the concept of minimal liner codes we proposed, this paper concentrates on irreducible cyclic codes and constructs the ideal access structures of the schemes based on the duals of minimal irreducible cyclic codes. In order to study the conditions whether several types of irreducible cyclic codes are minimal, we investigate the weight enumerators of certain irreducible cyclic codes by means of cyclotomic classes and Gaussian periods. On the basis of our aforementioned studies, we obtain ideal access structures and show the corresponding examples through programming.