Bounds and constructions for [formula omitted]-OOCs

Abstract

In 1996, Yang introduced variable-weight optical orthogonal code for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. Let W={w1,…,wr} be an ordering of a set of r integers greater than 1, λ be a positive integer (auto- and cross-correlation parameter), and Q=(q1,…,qr) be an r-tuple (weight distribution sequence) of positive rational numbers whose sum is 1. A (v,W,λ,Q) variable-weight optical orthogonal code ((v,W,λ,Q)-OOC) is a collection of (0,1) sequences with weights in W, auto- and cross-correlation parameter λ. Some work has been done on the construction of optimal (v,W,1,Q)-OOCs, while little is known on the construction of (v,W,λ,Q)-OOCs with λ≥2. It is well known that (v,W,λ,Q)-OOCs with λ≥2 have much bigger cardinality than those of (v,W,1,Q)-OOCs for the same v,W,Q. In this paper, a new upper bound on the number of codewords of (v,W,λ,Q)-OOCs is given, and infinite classes of optimal (v,{3,4},2,Q)-OOCs are constructed.