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Large sets of disjoint group‐divisible designs with block size three and type 2 n 4 1
Author(s) -
Cao H.,
Lei J.,
Zhu L.
Publication year - 2001
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.1012
Subject(s) - mathematics , disjoint sets , combinatorics , block (permutation group theory) , block size , group (periodic table) , type (biology) , combinatorial design , discrete mathematics , cryptography , arithmetic , algorithm , computer science , key (lock) , ecology , chemistry , computer security , organic chemistry , biology
Large sets of disjoint group‐divisible designs with block size three and type 2 n 4 1 have been studied by Schellenberg, Chen, Lindner and Stinson. These large sets have applications in cryptography in the construction of perfect threshold schemes. It is known that such large sets can exist only for n ≡ 0 ( mod 3) and do exist for n = 6 and for all n = 3 k , k ≥ 1. In this paper, we present new recursive constructions and use them to show that such large sets exist for all odd n ≡ 0 ( mod 3) and for even n = 24 m , where m odd ≥ 1. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 285–296, 2001