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Generalized Steiner systems GS4 (2, 4, v, g) for g = 2, 3, 6

✍ Scribed by D. Wu; G. Ge; L. Zhu

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 211 KB
Volume: 9
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.1020

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✦ Synopsis

Generalized Steiner systems GS d tY kY vY g were ®rst introduced by Etzion and used to construct optimal constant-weight codes over an alphabet of size g 1 with minimum Hamming distance d, in which each codeword has length v and weight k. Much work has been done for the existence of generalized Steiner triple systems GS2Y 3Y vY g. However, for block size four there is not much known on GS d 2Y 4Y vY g. In this paper, the necessary conditions for the existence of a GS d tY kY vY g are given, which answers an open problem of Etzion. Some singular indirect product constructions for GS d 2Y kY vY g are also presented. By using both recursive and direct constructions, it is proved that the necessary conditions for the existence of a GS 4 2Y 4Y vY g are also suf®cient for g 2Y 3Y 6X

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