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Generalized steiner triple systems with group size five
Author(s) -
Chen K.,
Ge G.,
Zhu L.
Publication year - 1999
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/(sici)1520-6610(1999)7:6<441::aid-jcd5>3.0.co;2-w
Subject(s) - mathematics , steiner system , combinatorics , alphabet , constant (computer programming) , group (periodic table) , discrete mathematics , computer science , chemistry , organic chemistry , philosophy , linguistics , programming language
Generalized Steiner triple systems, GS(2, 3, n , g ) are used to construct maximum constant weight codes over an alphabet of size g +1 with distance 3 and weight 3 in which each codeword has length n . The existence of GS(2, 3, n , g ) has been solved for g =2, 3, 4, 9. In this paper, by introducing a special kind of holey generalized Steiner triple systems (denoted by HGS(2, 3, ( n , u ), g )), singular indirect product (SIP) construction for GDDs is used to construct generalized Steiner systems. The numerical necessary conditions for the existence of a GS(2, 3, n , g ) are shown to be sufficient for g =5.