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Generalized Steiner systems GS 4 (2, 4, v, g) for g = 2, 3, 6
Author(s) -
Wu D.,
Ge G.,
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.1020
Subject(s) - mathematics , combinatorics , alphabet , steiner system , constant (computer programming) , code word , hamming distance , discrete mathematics , decoding methods , statistics , philosophy , linguistics , computer science , programming language
Generalized Steiner systems GS d ( t, k, v, g ) were first 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 GS(2, 3, v , g ). However, for block size four there is not much known on GS d (2, 4, v , g ). In this paper, the necessary conditions for the existence of a GS d ( t, k, v, g ) are given, which answers an open problem of Etzion. Some singular indirect product constructions for GS d (2, k, v, 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 (2, 4, v , g ) are also sufficient for g = 2, 3, 6. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 401–423, 2001