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On optimal superimposed codes
Author(s) -
Kim Hyun Kwang,
Lebedev Vladimir
Publication year - 2003
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.10056
Subject(s) - mathematics , intersection (aeronautics) , combinatorics , incidence matrix , code (set theory) , cover (algebra) , cryptography , discrete mathematics , set (abstract data type) , binary number , binary code , key (lock) , arithmetic , algorithm , computer science , computer security , structural engineering , mechanical engineering , node (physics) , engineering , programming language , aerospace engineering
A ( w,r ) cover‐free family is a family of subsets of a finite set such that no intersection of w members of the family is covered by a union of r others. A binary ( w,r ) superimposed code is the incidence matrix of such a family. Such a family also arises in cryptography as a concept of key distribution patterns. In this paper, we develop a method of constructing superimposed codes and prove that some superimposed codes constructed in this way are optimal. © 2003 Wiley Periodicals, Inc. J Combin Designs 12: 79–71, 2004.