Search

Let $W=\{w_{1}, \ldots , w_{r}\}$ be a set of positive integers, $\lambda _{c}$ a positive integer, $\Lambda _{a}=(\lambda _{a}^{(1)}, \ldots \lambda _{a}^{(r)})$ an $r$ -tuple of positive integers, and $Q=(q_{1}, \ldots q_{r})$ an $r$ -tuple of positive rational numbers whose sum is 1. In 1996, Yang introduced variable-weight optical orthogonal code, $(n, W, \Lambda _{a}, \lambda _{c}, Q)$ -OOC, for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. Some work had been done on the constructions of optimal $(n, W, \Lambda _{a}, 1, Q)$ -OOCs with unequal auto-correlation constraints for $W=\{3, 4\}$ and {3, 5}, while little is known on optimal $(n, W, \Lambda _{a}, 1, Q)$ -OOCs for $|W|\geq 3$ . In this paper, we focus our main attentions on $(n, \{3, 4, 5\}, \Lambda _{a}, 1, Q)$ -OOCs with $\Lambda _{a}\in \{(2, 1, 1), (2, 1, 2), (2, 2, 1), (2, 2, 2)\}$ . Tight upper bounds on the maximum code size of $(n, \{3, 4, 5\}, \Lambda _{a}, 1, Q)$ -OOCs are obtained, and infinite classes of optimal $(n, \{3, 4, 5\}, \Lambda _{a}, 1, Q)$ -OOCs are constructed.

Zero-difference balanced (ZDB) functions were introduced recently by Ding for the construction of optimal constant-composition codes, and optimal and perfect difference systems of sets. They are closely related to partitioned difference families. In this paper, we present generic constructions of ZDB functions from functions with difference-balanced property. In particular, two classes of ZDB functions with new and flexible parameters are reported. Employing these new ZDB functions, we obtain at the same time optimal (1) constant-composition codes, (2) constant-weight codes, and (3) perfect difference systems of sets, all with new and flexible parameters.

Variable-weight optical orthogonal code (OOC) was introduced by Yang for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. In this paper, four general constructions for optimal cyclic packings and optimal variable-weight OOCs are presented. Many new infinite classes of optimal (v, W,1,Q)-OOCs are obtained. New infinite classes of optimal (v, W,1,Q)-OOCs for |W| ≥ 4 are easily obtained by the constructions.

Variable-weight optical orthogonal code (OOC) was introduced by Yang for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. In this paper, the upper bound on the size of variable-weight OOCs is improved, a cyclic t-(v, W, λ, Q) packing is introduced to construct a variable-weight OOC, an upper bound for the number of blocks of t-(v, W, λ, Q) packings is obtained, and an equivalence between optimal cyclic packing and optimal variable-weight optical orthogonal code is established. Recursive constructions for optimal 2-CP(W, 1, Q;v)s are also presented. By using skew starters and these constructions, infinite classes of optimal (v, W, 1, {1/2, 1/2})-OOCs are obtained for W = {3, 4}, and {4, 5}.