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Large sets of disjoint group-divisible designs with block size three and type 2n41

✍ Scribed by H. Cao; J. Lei; L. Zhu

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 141 KB
Volume: 9
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.1012

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✦ Synopsis

Abstract

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

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