Rongcun Qin

In the last decade many variants of the well-known notion of an optical orthogonal code (OOC) have been studied. In particular, it was allowed to have variable weights and that codewords of different weight may have different autocorrelation parameters so that one should speak of 'autocorrelation function' rather than 'autocorrelation parameter'. In this paper we investigate OOCs with two weights 4 and 5, autocorrelation function with values in $ \{1, 2\} $, and crosscorrelation parameter one. After giving tight upper bounds on their maximum size, we construct some infinite classes reaching optimality with as many codewords of weight 4 as many codewords of weight 5.

Let $ m $, $ n $ be positive integers, and $ K $ a set of positive integers with size greater than 2. An $ (m,n,K,1) $ optical orthogonal signature pattern code, $ (m,n,K,1) $-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 $ G $ be an additive group, a balanced $ (G, K, 1) $ difference packing, $ (G, K, 1) $-BDP, can be used to construct a balanced $ (m,n,K,1) $-OOSPC when $ G = {\mathbb{Z}}_m\times {\mathbb{Z}}_n $. In this paper, the existences of optimal $ ( {\mathbb{Z}}_{2u}\times {\mathbb{Z}}_{38v}, \{3,4,5\},1) $-BDPs are completely solved with $ u, \ v\equiv 1\pmod2 $, and the corresponding optimal balanced $ (2u, 38v,\{3,4,5\},1) $-OOSPCs are also obtained.

Multilength variable-weight optical orthogonal codes(MLVWOOCs) are recently proposed for supporting multirate and integrated multimedia services in optical code division multiple access (OCDMA) networks. Some work had been done on MLVWOOCs with weight set $ W = \{3, 4\} $, $ \{3, 5\} $. In this paper, we consider MLVWOOCs with $ W = \{4, 5\} $, and some several infinite classes of optimal MLVWOOCs are 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 $ (m, n, \{3, 4\}, 1) $-OOSPCs. In this paper, it is proved that there exist optimal balanced $ (2u, 16v, \{4, 5\}, 1) $-OOSPCs for odd integers $ u\geq 1 $, $ v\geq 1 $.