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×v,W,1,Q)(u×v,W,1,Q)-OOSPC is improved. By using quadratic residues and skew starters, some direct constructions for balanced (3×gv,3×g,{3,4},1)(3×gv,3×g,{3,4},1)-OOSPCs are given for some positive integers gg and vv. Several recursive constructions for balanced (u×v,W,1)(u×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×9v,{3,4},1)(3u×9v,{3,4},1)-OOSPC is obtained for any pair of positive integers (u,v)(u,v) with gcd(u,3)=1gcd(u,3)=1.