排序方式: 共有28条查询结果,搜索用时 46 毫秒
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Ross Anderson Cunsheng Ding Tor Helleseth Torleiv Klove 《Designs, Codes and Cryptography》1998,15(2):111-124
Previous researchers have designed shared control schemes with a view to minimising the likelihood that participants will conspire to perform an unauthorised act. But, human nature being what it is, systems inevitably fail; so shared control schemes should also be designed so that the police can identify conspirators after the fact. This requirement leads us to search for schemes with sparse access structures. We show how this can be done using ideas from coding theory. In particular, secret sharing schemes based on geometric codes whose dual [n,k,d] codes have d and n as their only nonzero weights are suitable. We determine their access structures and analyse their properties. We have found almost all of them, and established some relations among codes, designs and secret-sharing schemes. 相似文献
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In this paper, a construction of optimal constant composition codes is developed, and used to derive some series of new optimal
constant composition codes meeting the upper bound given by [13]. 相似文献
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External difference families (EDFs) are a type of new combinatorial designs originated from cryptography. In this paper, some
earlier ideas of recursive and cyclotomic constructions of combinatorial designs are extended, and a number of classes of
EDFs and disjoint difference families are presented. A link between a subclass of EDFs and a special type of (almost) difference
sets is set up. 相似文献
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A family of skew Hadamard difference sets 总被引:1,自引:0,他引:1
Cunsheng Ding 《Journal of Combinatorial Theory, Series A》2006,113(7):1526-1535
In 1933 a family of skew Hadamard difference sets was described by Paley using matrix language and was called the Paley-Hadamard difference sets in the literature. During the last 70 years, no new skew Hadamard difference sets were found. It was conjectured that there are no further examples of skew Hadamard difference sets. This conjecture was proved to be true for the cyclic case in 1954, and further progress in favor of this conjecture was made in the past 50 years. However, the conjecture remains open until today. In this paper, we present a family of new perfect nonlinear (also called planar) functions, and construct a family of skew Hadamard difference sets using these perfect nonlinear functions. We show that some of the skew Hadamard difference sets presented in this paper are inequivalent to the Paley-Hadamard difference sets. These new examples of skew Hadamard difference sets discovered 70 years after the Paley construction disprove the longstanding conjecture on skew Hadamard difference sets. The class of new perfect nonlinear functions has applications in cryptography, coding theory, and combinatorics. 相似文献
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The objectives of this paper are to survey and extend earlier results on the weight distributions of irreducible cyclic codes, present a divisibility theorem and develop bounds on the weights in irreducible cyclic codes. 相似文献
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Cunsheng Ding 《Designs, Codes and Cryptography》2018,86(3):703-719
It has been known for a long time that t-designs can be employed to construct both linear and nonlinear codes and that the codewords of a fixed weight in a code may hold a t-design. While a lot of progress in the direction of constructing codes from t-designs has been made, only a small amount of work on the construction of t-designs from codes has been done. The objective of this paper is to construct infinite families of 2-designs and 3-designs from a type of binary linear codes with five weights. The total number of 2-designs and 3-designs obtained in this paper are exponential in any odd m and the block size of the designs varies in a huge range. 相似文献
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Skew Hadamard difference sets have been an interesting topic of study for over 70 years. For a long time, it had been conjectured the classical Paley difference sets (the set of nonzero quadratic residues in where ) were the only example in Abelian groups. In 2006, the first author and Yuan disproved this conjecture by showing that the image set of is a new skew Hadamard difference set in with m odd, where denotes the first kind of Dickson polynomials of order n and . The key observation in the proof is that is a planar function from to for m odd. Since then a few families of new skew Hadamard difference sets have been discovered. In this paper, we prove that for all , the set is a skew Hadamard difference set in , where m is odd and . The proof is more complicated and different than that of Ding‐Yuan skew Hadamard difference sets since is not planar in . Furthermore, we show that such skew Hadamard difference sets are inequivalent to all existing ones for by comparing the triple intersection numbers. 相似文献