On Block Sequences of Steiner Quadruple Systems with Error Correcting Consecutive Unions | Zendy

Gennian Ge | Zendy; Ying Miao | Zendy; Xiande Zhang | Zendy

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On Block Sequences of Steiner Quadruple Systems with Error Correcting Consecutive Unions

Author(s) -

Gennian Ge,

Ying Miao,

Xiande Zhang

Publication year - 2009

Publication title -

siam journal on discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.843

H-Index - 66

eISSN - 1095-7146

pISSN - 0895-4801

DOI - 10.1137/08071750x

Subject(s) - combinatorics , mathematics , sequence (biology) , block (permutation group theory) , discrete mathematics , code (set theory) , computer science , genetics , set (abstract data type) , biology , programming language

Motivated by applications in combinatorial group testing for consecutive positives,we investigate a block sequence of a maximum packing MP(t, k, v) which contains the blocks exactlyonce such that the collection of all blocks together with all unions of two consecutive blocks of thissequence forms an error correcting code with minimum distance d. Such a sequence is usually called ablock sequence with consecutive unions having minimum distance d, and denoted by BSCU(t, k, vd).In this paper, we show that the necessary conditions for the existence of BSCU(3, 4, v4)s of Steinerquadruple systems, namely, v ≡ 2,4 (mod 6) and v ≥ 4, are also sufficient, excepting v = 8, 10

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