关键词: 极小线性码, 存取结构, 极小码字, 秘密共享方案, 不可约循环码

Abstract: Theoretically,every linear code can be used to construct secret sharing schemes.However,determining the access structure of the schemes based on linear codes is very hard.The concept of minimal linear code is proposed,which makes the determination of the access structure of the schemes based on the duals of minimal linear codes easier.It is shown that the shortening codes of minimal linear codes are minimal as well.Then the conditions whether several types of irreducible cyclic codes are minimal or not are presented.Furthermore,the access structures of secret sharing schemes based on the duals of minimal linear codes are studied.Finally,the access structures of the schemes in specific examples are obtained through programming.

Key words: minimal linear code, access structures, minimal codeword, secret sharing scheme, irreducible cyclic codes