Premium
Some new results on superimposed codes
Author(s) -
Kim Hyun Kwang,
Lebedev Vladimir,
Oh Dong Yeol
Publication year - 2005
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.20029
Subject(s) - mathematics , code (set theory) , intersection (aeronautics) , combinatorics , uniqueness , discrete mathematics , set (abstract data type) , cover (algebra) , computer science , mathematical analysis , geography , mechanical engineering , engineering , programming language , cartography
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 ( w , r ) superimposed code is the incidence matrix of such a family. Such a family also arises in cryptography as the concept of key distribution pattern. In the present paper, we give some new results on superimposed codes. First we construct superimposed codes from super‐simple designs which give us results better than superimposed codes constructed by other known methods. Next we prove the uniqueness of the (1,2) superimposed code of size 9 × 12, the (2,2) superimposed code of size 14 × 8, and the (2,3) superimposed code of size 30 × 10. Finally, we improve numerical values of upper bounds for the asymptotic rate of some ( w , r ) superimposed codes. © 2004 Wiley Periodicals, Inc.