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<jats:title>Abstract</jats:title><jats:p>In [<jats:ext-link xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#bib3">3</jats:ext-link>], a general recursive construction for optical orthogonal codes is presented, that guarantees to approach the optimum asymptotically if the original families are asymptotically optimal. A challenging problem on OOCs is to obtain optimal OOCs, in particular with λ > 1. Recently we developed an algorithmic scheme based on the maximal clique problem (MCP) to search for optimal (<jats:italic>n</jats:italic>, 4, 2)‐OOCs for orders up to <jats:italic>n</jats:italic> = 44. In this paper, we concentrate on recursive constructions for optimal (<jats:italic>n</jats:italic>, 4, 2)‐OOCs. While “most” of the codewords can be constructed by general recursive techniques, there remains a gap in general between this and the optimal OOC. In some cases, this gap can be closed, giving recursive constructions for optimal (<jats:italic>n</jats:italic>, 4, 2)‐OOCs. This is predicated on reducing a series of recursive constructions for optimal (<jats:italic>n</jats:italic>, 4, 2)‐OOCs to a single, finite maximal clique problem. By solving these finite MCP problems, we can extend the general recursive construction for OOCs in [<jats:ext-link xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#bib3">3</jats:ext-link>] to obtain new recursive constructions that give an optimal (<jats:italic>n</jats:italic> · 2<jats:sup><jats:italic>x</jats:italic></jats:sup>, 4, 2)‐OOC with <jats:italic>x</jats:italic> ≥ 3, if there exists a <jats:italic>CSQS</jats:italic>(<jats:italic>n</jats:italic>). © 2004 Wiley Periodicals, Inc.</jats:p>
収録刊行物
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- Journal of Combinatorial Designs
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Journal of Combinatorial Designs 12 (5), 333-345, 2004-01
Wiley