Combinatorial constructions for optimal multiple-weight optical orthogonal signature pattern codes

Multiple-weight (MW) optical orthogonal signature pattern code (OOSPC) was introduced by Kwong and Yang for 2-D image transmission in multicore-fiber optical code-division multiple-access (OCDMA) networks with multiple quality of services (QoS) requirement. In this paper, an upper bound on the maximum code size of (u x v, W, 1, Q)-OOSPC is improved. By using quadratic residues and skew starters, some direct constructions for balanced (3 x gv, 3 x g, {3, 4}, 1)-OOSPCs are given for some positive integers g and v. Several recursive constructions for balanced (u x v, W, 1)-OOSPCs are presented by means of incomplete difference matrices and perfect relative difference families. By using those constructions, a balanced optimal (3u x 9v, {3, 4}, 1)-OOSPC is obtained for any pair of positive integers (u, v) with gcd(u, 3) = 1. (C) 2015 Elsevier B.V. All rights reserved.