
A (nxm, k, ?) two-dimensional optical orthogonal code (2-D OOC), C, is a family of nxm (0, 1)-arrays of constant weight k such that ?i=1n?j=0m-1A(i, j)B(i, j?m?) ? ? for any arrays A, B in C and any integer ? except when A = B and ? ? 0 (mod m ), where ?m denotes addition modulo m. Such codes are of current practical interest as they enable optical communication at lower chip rate. To simplify practical implementation, the AM-OPPW (at most one-pulse per wavelength) restriction is often appended to a 2-D OOC. An AM-OPPW 2-D OOC is optimal if its size is the largest possible. In this paper, the notion of a perfect AM-OPPW 2-D OOC is proposed, which is an optimal (nxm, k, ?) AM-OPPW 2-D OOC with cardinality [(m ? n(n-1)...(n-?))/(k(k-1)...(k-?))] . A link between optimal (nxm, k, ?) AM-OPPW 2-D OOCs and block designs is developed. Some new constructions for such optimal codes are described by means of semicyclic group divisible designs. Several new infinite families of perfect (nxm, k, 1) AM-OPPW 2-D OOCs with k ? {2, 3, 4} are thus produced.
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 26 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Top 10% | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Top 10% |
