### Abstract

In [3], 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 k > 1. Recently we developed an algorithmic scheme based on the maximal clique problem (MCP) to search for optimal (n; 4; 2)-OOCs for orders up to n = 44. In this paper, we concentrate on recursive constructions for optimal (n; 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 (n; 4; 2)-OOCs. This is predicated on reducing a series of recursive constructions for optimal (n; 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 [3] to obtain new recursive constructions that give an optimal (n 2x; 4; 2)-OOC with x ≥ 3, if there exists a CSQS(n).

Original language | English (US) |
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Pages (from-to) | 333-345 |

Number of pages | 13 |

Journal | Journal of Combinatorial Designs |

Volume | 12 |

Issue number | 5 |

DOIs | |

State | Published - Dec 1 2004 |

### Keywords

- Cyclic t-designs
- Matched factor systems
- Maximal clique problems
- Optical orthogonal codes

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

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## Cite this

*Journal of Combinatorial Designs*,

*12*(5), 333-345. https://doi.org/10.1002/jcd.20003