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Let \begin{document}$ m $\end{document}, \begin{document}$ n $\end{document} be positive integers, and \begin{document}$ K $\end{document} a set of positive integers with size greater than 2. An \begin{document}$ (m,n,K,1) $\end{document} optical orthogonal signature pattern code, \begin{document}$ (m,n,K,1) $\end{document}-OOSPC, was introduced by Kwong and Yang for 2-D image transmission in multicore-fiber optical code-division multiple-access (OCDMA) networks with multiple quality of services (QoS) requirement. Let \begin{document}$ G $\end{document} be an additive group, a balanced \begin{document}$ (G, K, 1) $\end{document} difference packing, \begin{document}$ (G, K, 1) $\end{document}-BDP, can be used to construct a balanced \begin{document}$ (m,n,K,1) $\end{document}-OOSPC when \begin{document}$ G = {\mathbb{Z}}_m\times {\mathbb{Z}}_n $\end{document}. In this paper, the existences of optimal \begin{document}$ ( {\mathbb{Z}}_{2u}\times {\mathbb{Z}}_{38v}, \{3,4,5\},1) $\end{document}-BDPs are completely solved with \begin{document}$ u, \ v\equiv 1\pmod2 $\end{document}, and the corresponding optimal balanced \begin{document}$ (2u, 38v,\{3,4,5\},1) $\end{document}-OOSPCs are also obtained.

Kitayama proposed a novel OCDMA (called spatial CDMA) for parallel transmission of 2-D images through multicore fiber. Optical orthogonal signature pattern codes (OOSPCs) play an important role in this CDMA network. 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) requirements. Some results had been done on optimal balanced \begin{document}$ (m, n, \{3, 4\}, 1) $\end{document} -OOSPCs. In this paper, it is proved that there exist optimal balanced \begin{document}$ (2u, 16v, \{4, 5\}, 1) $\end{document} -OOSPCs for odd integers \begin{document}$ u\geq 1 $\end{document} , \begin{document}$ v\geq 1 $\end{document} .

Let \begin{document}$ W = \{w_1, w_2, \cdots, w_r\} $\end{document} be a set of \begin{document}$ r $\end{document} integers greater than 1, \begin{document}$ \Lambda_a = (\lambda_a^{(1)}, \lambda_a^{(2)}, \cdots, \lambda_a^{(r)}) $\end{document} be an \begin{document}$ r $\end{document} -tuple of positive integers, \begin{document}$ \lambda_c $\end{document} be a positive integer, and \begin{document}$ Q = (q_1, q_2, \cdots, q_r) $\end{document} be an \begin{document}$ r $\end{document} -tuple of positive rational numbers whose sum is 1. Variable-weight optical orthogonal code ( \begin{document}$ (n, W, \Lambda_a, \lambda_c, Q) $\end{document} -OOC) was introduced by Yang for multimedia optical CDMA systems with multiple quality of service requirements. In this paper, tight upper bounds on the maximum code size of \begin{document}$ (n, \{3, 4, 5\}, \Lambda_a, 1, Q) $\end{document} -OOCs are obtained, and infinite classes of optimal \begin{document}$ (n, \{3, 4, 5\}, \Lambda_a, 1, Q) $\end{document} -OOCs are constructed.

Variable-weight optical orthogonal code (OOC) was introduced by Yang for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. It is proved that optimal $(v, \{3, 5\}, 1, (1/2, 1/2))$-OOCs exist for some complete congruence classes of $v$. In this paper, for $Q\in \{(2/3,1/3), (3/4,1/4)\}$, by using skew starters, it is also proved that optimal $(v, \{3,5\}, 1, Q)$-OOCs exist for some complete congruence classes of $v$.

A pair of binary sequences is generalized from the concept of a two-level autocorrelation function of single binary sequence. In this paper, we describe two classes of binary sequence pairs of period $N=2q$, where $q=4f+1$ is an odd prime and $f$ is an even integer. Those classes of binary sequence pairs are based on cyclic almost difference set pairs. They have optimal three-level cross-correlation, and either balanced or almost balanced.