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arXiv 1202.4058cs.CR
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一类极小线性码的秘密共享

Secret sharing with a class of minimal linear codes

Yun Song, Zhihui Li

摘要:

构造秘密共享方案的方法有很多种,其中一种是基于编码理论。理论上,任何线性码都可以用来构造秘密共享方案。然而,一般来说,基于线性码的方案的访问结构的确定是非常困难的。本文提出了最小线性码的概念,使得基于最小线性码的方案的存取结构的确定变得容易。证明了极小线性码的缩短码也是极小线性码。然后给出了几类不可约循环码是极小线性码的条件。进一步研究了基于最小线性码的秘密共享方案的访问结构,并通过编程得到了具体实例中的访问结构。

英文摘要:

There are several methods for constructing secret sharing schemes, one of which is based on coding theory. Theoretically, every linear code can be used to construct secret sharing schemes. However, in general, determining the access structures of the schemes based on linear codes is very hard. This paper proposed the concept of minimal linear code, which makes the determination of the access structures of the schemes based on the duals of minimal linear codes easier. It is proved that the shortening codes of minimal linear codes are also minimal ones. Then the conditions whether several types of irreducible cyclic codes are minimal linear codes are presented. Furthermore, the access structures of secret sharing schemes based on the duals of minimal linear codes are studied, and these access structures in specific examples are obtained through programming.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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