Recursive constructions for optimal (n, 4, 2)-OOCs

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).