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Generalized steiner triple systems with group size five

✍ Scribed by K. Chen; G. Ge; L. Zhu

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 154 KB
Volume: 7
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1999)7:6<441::aid-jcd5>3.0.co;2-w

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✦ Synopsis

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 suf®cient for g 5.

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