Secret sharing schemes from binary linear codes

Li, Zhihui; Xue, Tao; Liu, Hong

doi:10.1016/j.ins.2010.07.029

Cited by 22 publications

(19 citation statements)

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“…A codeword c 2 covers a codeword c 1 if the support of c 2 contains that of c 1 . 15]). If a nonzero codeword c covers only its multiples, but no other nonzero codewords, then it is called a minimal vector.…”

Section: Minimal Linear Codes and Their Constructionmentioning

confidence: 99%

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Ideal access structures based on a class of minimal linear codes

Song

2015

International Journal of Computer Mathematics

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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 concentrate on irreducible cyclic codes and construct 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.

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Section: Minimal Linear Codes and Their Constructionmentioning

confidence: 99%

“…The properties and determination of minimal linear codes are exhibited in [15]. We recall them without proofs.…”

Section: Minimal Linear Codes and Their Constructionmentioning

confidence: 99%

Ideal access structures based on a class of minimal linear codes

Song

2015

International Journal of Computer Mathematics

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“…So such a two-weight code can be used to construct secret sharing schemes, which is an interesting subject of cryptography [5,11].…”

Section: Some Applicationsmentioning

confidence: 99%

Further results on support weights of certain subcodes

Liu

Chen

Sun

et al. 2010

Des. Codes Cryptogr.

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“…The minimum weight code word problem requires one to find a minimum weight code word, given a basis of the code. This problem is important for several reasons: a minimum weight code word is a measure of the error correction capability of the code [9], also, codes with large minimum weight code words have applications in diverse areas such as cryptography [18,17,16], pseudorandom generators [1,11].…”

Section: Introductionmentioning

confidence: 99%

Performance of metropolis algorithm for the minimum weight code word problem

Shenoy

Biswas

Kurur

2014

Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation

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We study the performance of the Metropolis algorithm for the problem of finding a code word of weight less than or equal to M , given a generator matrix of an [n, k]-binary linear code. The algorithm uses the set S k of all k × k invertible matrices as its search space where two elements are considered adjacent if one can be obtained from the other via an elementary row operation (i.e by adding one row to another or by swapping two rows.) We prove that the Markov chains associated with the Metropolis algorithm mix rapidly for suitable choices of the temperature parameter T . We ran the Metropolis algorithm for a number of codes and found that the algorithm performed very well in comparison to previously known experimental results.

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Secret sharing schemes from binary linear codes

Cited by 22 publications

References 20 publications

Ideal access structures based on a class of minimal linear codes

Ideal access structures based on a class of minimal linear codes

Further results on support weights of certain subcodes

Performance of metropolis algorithm for the minimum weight code word problem

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