Families of Finite Sets in which No Intersection of ℓ Sets Is Covered by the Union of s Others

Journal of Combinatorial Theory, Series A - Tập 99 Số 2 - Trang 195-218 - 2002
A.G. D'yachkov1, P.A. Vilenkin1, David C. Torney2, Anthony J. Macula3
1Department of Probability Theory, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119899, [email protected]@vilenkin.dnttm.ruf2
2Department of Mathematics, State University of New York, College at Geneseo, Geneseo, New York, 14454, [email protected]
3MS K710, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, [email protected]

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Tài liệu tham khảo

Du, 1993

D'yachkov, 1982, Bounds on the length of disjunct codes, Problemy Peredachi Informatsii, 17, 7

D'yachkov, 1983, A survey of superimposed code theory, Problems Control Inform. Theory, 12, 229

D'yachkov, 1989, Superimposed distance codes, Problems Control Inform. Theory, 18, 237

D'yachkov, 2000, New constructions of superimposed codes, IEEE Trans. Inform. Theory, 46, 284, 10.1109/18.817530

D'yachkov, 2000, New applications and results of superimposed code theory arising from the potentialities of molecular biology

D'yachkov, 2000, New results in the theory of superimposed codes, 7th International Workshop (Algebraic and Combinatorial Coding Theory), Bansko, Bulgaria, 126

D'yachkov, 2001, Two models of nonadaptive group testing for designing screening experiments, 10.1007/978-3-642-57576-1_8

Engel, 1996, Interval packing and covering in the Boolean lattice, Combin. Probab. Comput., 5, 373, 10.1017/S0963548300002121

Erdos, 1982, Families of finite sets in which no set is covered by the union of two others, J. Combin. Theory Ser. A, 33, 158, 10.1016/0097-3165(82)90004-8

Erdos, 1985, Families of finite sets in which no set is covered by the union of r others, Israel J. Math., 51, 75, 10.1007/BF02772959

Furedi, 1996, A note of r-cover-free families, J. Combin. Theory Ser. A, 73, 172, 10.1006/jcta.1996.0012

Gallager, 1968

Kautz, 1964, Nonrandom binary superimposed codes, IEEE Trans. Inform. Theory, 10, 363, 10.1109/TIT.1964.1053689

H. K. Kim, and, V. S. Lebedev, On optimal cover-free families, superimposed codes and key distribution patterns, J. Combin. Theory Ser. A, submitted.

MacWilliams, 1983

Nguyen Quang, 1988, Bounds on constant weight binary superimposed codes, Problems Control Inform. Theory, 17, 223

Ruszinko, 1994, On the upper bound of the size of r-cover-free families, J. Combin. Theory Ser. A, 66, 302, 10.1016/0097-3165(94)90067-1

1994, Problemy Peredachi Informatsii, 30, 14

Stinson, 2000, Some new bounds for cover-free families, J. Combin. Theory Ser. A, 90, 224, 10.1006/jcta.1999.3036

P. A. Vilenkin, Asymptotic Problems of Combinatorial Coding Theory and Information Theory, Ph.D. dissertation, Moscow State University, 2001.