基于极小线性码上的秘密共享方案

从理论上说,每个线性码都可用于构造秘密共享方案,但是在一般情况下,所构造的秘密共享方案的存取结构是难以确定的.本文提出了极小线性码的概念,指出基于这种码的对偶码所构造的秘密共享方案的存取结构是容易确定的.本文首先证明了极小线性码的缩短码一定是极小线性码.然后对几类不可约循环码给出它们为极小线性码的判定条件,并在理论上研究了基于几类不可约循环码的对偶码上的秘密共享方案的存取结构.最后用编程具体求出了一些实例中方案的存取结构.

Secret Sharing Schemes Based on Minimal Linear Codes

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.