Bounds and constructions for optimal variable-weight OOCs with unequal auto-And cross-correlation constraints
Abstract
Let W = {W1,...,Wr} be an ordering of a set of r integers greater than 1, a = (λa(1),..., λa(r))) be an r-Tuple of positive integers, λc be a positive integer, and Q = (qi,..., qr) be an r-Tuple of positive rational numbers whose sum is 1. In 1996, Yang introduced variable-weight optical orthogonal code ((n, W, a, λc, Q)-OOC) for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. Most existing works on variable-weight optical orthogonal codes assume that λa(1)...,λa(r) = λc = 1. In this paper, we focus our attention on (n, {3,4}, λa, l,Q)-OOCs, where a ϵ {(1,2), (2,1),(2,2)}. Tight upper bounds on the maximum code size of (n, {3,4}, a 1, Q)-OOCs are obtained, and four infinite classes of optimal (n, {3,4}, a,1, Q)-OOCs are constructed. © 2015 Utilitas Mathematics.
