Bounds and constructions for -OOCs

In 1996, Yang introduced variable-weight optical orthogonal code for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. Let W = { w 1 , … , w r } be an ordering of a set of r integers greater than 1 , λ be a positive integer (auto- and cross-correlation parameter), and Q = ( q 1 , … , q r ) 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.