Some new results on superimposed codes

Kim, Hyun Kwang; Лебедев, В. С.; Oh, Dong Yeol

doi:10.1002/jcd.20029

Cited by 11 publications

(5 citation statements)

References 14 publications

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“…There are cases that the trivial solution given at the beginning of this section results in the optimal solutions. For example, from [13] and [23], we know that whenever t), T ) = T s , which implies that the trivial solution is an optimal solution. We list some of these optimal families in Table 4.2 (taken from [22,23]).…”

Section: Definition 44mentioning

confidence: 95%

“…For a fixed t ≥ 1 and a square prime power q with t < √ q − 1, there exists a sequence of (1, t)-CFF(n i q, q li−g+1 ) such that Next we describe the concatenated construction given in [23,47], which is a powerful method in constructing a larger cover-free family from small cover-free families. The notion of the separating matrix is equivalent to those of the separate code [22] and the separating hash family [47].…”

Section: Corollary 42mentioning

confidence: 99%

“…1 (taken from[23]) lists some numerical values of the upper bounds for the asymptotic rate R(s, t) which are the best results among several choices in Theorem 4.4.…”

mentioning

confidence: 98%

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Cover-Free Families and Their Applications

Ling¹,

Wang²,

Xing³

2007

Security in Distributed and Networking Systems

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Cover-free families are combinatorial objects that have been used in diverse applications such as information theory, communications, group testing, cryptography and information security. In this paper, we survey some mathematical results on cover-free families and present several interesting applications to topics in secure networks and distributed systems. IntroductionCover-free families were first studied in terms of superimposed binary codes by Kautz and Singleton [21] in 1964. These codes are related to retrieval files, data communication and magnetic memories. In 1985 Erdös, Frankl and Füredi [14] studied cover-free families as combinatorial objects, generalising the Sperner systems. Since then, they have been discussed by numerous researchers in the context of information theory, combinatorics, communication and cryptography and information security. In this paper we will present several interesting applications to topics in secure networks and distributed systems. Definition 4.1. Let X be a set of N elements (points) and let B be a 75 Security in Distributed and Networking Systems Downloaded from www.worldscientific.com by MCGILL UNIVERSITY on 06/22/16. For personal use only.

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Section: Definition 44mentioning

confidence: 95%

Section: Corollary 42mentioning

confidence: 99%

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Cover-Free Families and Their Applications

Ling¹,

Wang²,

Xing³

2007

Security in Distributed and Networking Systems

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“…Kim, Lebedev and Oh proved the uniqueness of the (9, 12, 1, 2) superimposed code in [6] and Oh proved the uniqueness of the (9, 11, 1, 2) superimposed code in [8].…”

Section: Engel Proved Inmentioning

confidence: 99%

On some Optimal (n,t,1,2) and (n,t,1,3) Super Imposed Codes

Manev¹

2009

SJC

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One of the main problems in the theory of superimposed codes is to find the minimum length N for which an (N, T,w, r) superimposed code exists for given values of T , w and r. Let N(T,w, r) be the minimum length N for which an (N, T,w, r) superimposed code exists. The (N, T,w, r) superimposed code is called optimal when N = N(T,w, r). The values of N(T, 1, 2) are known for T ≤ 12 and the values of N(T, 1, 3) are known for T ≤ 20. In this work the values of N(T, 1, 2) for 13 ≤ T ≤ 20 and the value of N(21, 1, 3) are obtained. The optimal superimposed codes with parameters (9, 10, 1, 2), (10, 13, 1, 2), (11, 14, 1, 2), (11, 15, 1, 2), (11, 16, 1, 2) and (11, 17, 1, 2) are classified up to equivalence. The optimal (N, T, 1, 3) superimposed codes for T ≤ 20 are classified up to equivalence.

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“…Vaccaro [9] studied this problem in a more general setup. Small values of generalized superimposed codes and and their relation to designs were considered by Kim, Lebedevin and Oh [51,52].…”

Section: Union-free and Cover-free Hypergraphsmentioning

confidence: 99%

Uniform hypergraphs containing no grids

Füredi¹,

Ruszinkó²

2013

Advances in Mathematics

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A hypergraph is called an r × r grid if it is isomorphic to a pattern of r horizontal and r vertical lines, i.e., a family of sets {A 1 , . . . , A r , B 1 , . . . , B r } such thatA hypergraph is linear, if |E ∩ F | ≤ 1 holds for every pair of edges.In this paper we construct large linear r-hypergraphs which contain no grids. Moreover, a similar construction gives large linear r-hypergraphs which contain neither grids nor triangles.For r ≥ 4 our constructions are almost optimal. These investigations are also motivated by coding theory: we get new bounds for optimal superimposed codes and designs. *

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Some new results on superimposed codes

Cited by 11 publications

References 14 publications

Cover-Free Families and Their Applications

Cover-Free Families and Their Applications

On some Optimal (n,t,1,2) and (n,t,1,3) Super Imposed Codes

Uniform hypergraphs containing no grids

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