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Chu, Wensong; Colbourn, Charles J.

Optimal \((n,4,2)\)-OOC of small orders. (English) Zbl 1044.05016

Discrete Math. 279, No. 1-3, 163-172 (2004).
Summary: We introduce an algorithmic scheme to find optimal (\(v,4,2\))-OOCs of small orders. We determine the sizes of optimal (\(v,4,2\))-OOCs up to \(v=44\), with three possible exceptions. We also develop an algebraic method to generate all difference triples over \(\mathbb{Z}_v\).

Cited in 14 Documents

MSC:

05B05 Combinatorial aspects of block designs
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)

Keywords:

Optical orthogonal codes; Cyclic Steiner quadruple systems; Maximal clique problem; \(r\)-simple matrices; Johnson bound
Cite Review PDF
Full Text: DOI

Online Encyclopedia of Integer Sequences:

Johnson bound J(n,4,2).
Maximal size of (n,4,2) optical orthogonal code.

References:

[1] Battiti, R.; Protasi, M., Reactive local search for the maximum clique problem, Algorithmica, 29, 4, 610-637 (2001) · Zbl 0985.68016
[2] Wensong Chu, Optical orthogonal codes and cyclic \(t\); Wensong Chu, Optical orthogonal codes and cyclic \(t\)
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[12] Lie Zhu, Private e-mail communication, 2001.; Lie Zhu, Private e-mail communication, 2001.
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