On complete arcs in Steiner systems S(2, 3, v) and S(2, 4, v)
نویسندگان
چکیده
منابع مشابه
Complete Arcs in Steiner Triple Systems
A complete arc in a design is a set of elements which contains no block, and is maximal with respect to this property. The spectrum of sizes of complete arcs in Steiner triple systems is determined without exception here.
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We survey the basic properties and results on Steiner systems S(2, 4, v), as well as open problems.
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Generalized Steiner systems GS(2, 4, v, 2) were first discussed by Etzion and used to construct optimal constant weight codes over an alphabet of size three with minimum Hamming distance five, in which each codeword has length v and weight four. Etzion conjectured its existence for any integer v ≥ 7 and v ≡ 1 (mod 3). The conjecture has been verified for prime powers v > 7 and v ≡ 7 (mod 12) by...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1989
ISSN: 0012-365X
DOI: 10.1016/0012-365x(89)90352-x