New optical orthogonal signature pattern codes with maximum collision parameter 2 and weight 4
New optical orthogonal signature pattern codes with maximum collision parameter 2 and weight 4
复制标题
具有最大碰撞参数 2 和权重 4 的新光学正交签名模式代码
DOI：
10.1007/s10623-016-0310-8
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发表时间：
2017-11-01
影响因子：
1.6
通讯作者：
Li, Yun
中科院分区：
文献类型：
--
作者：
Chen, Jingyuan;Ji, Lijun;Li, Yun
光正交签名模式码（OOSPC）在一种新型的二维图像光码分多址网络中起着重要的作用。一个-OOSPC和一个-（mn，w，1）填充设计之间存在一一对应的关系，该填充设计允许一个同构于的自同构群。在2010年，Sawa利用一个单因子的科勒图构造了一个（m，n，4，2）-OOSPC，其中该图包含一个唯一的2阶元素。本文研究了具有三个二阶元素的科勒图的单因子存在性。证明了如果存在一个2 p阶S-循环Steiner四元组系，其中是素数，则在相对于Sylow 2-子群的科勒图中存在一个单因子.利用这个单因子，我们构造了一个相对于Sylow 2-子群的严格不变正则。利用已知的S-循环SQS（2 p）和严格不变正则G-设计的递归构造，我们构造了更严格不变的3-（mn，4，1）填充设计.因此，对于任何带，都有一个最优的-OOSPC和一个最优的（6 m，6 n，4，2）-OOSPC，其中m，n是奇数，其集合中的所有素因子都是素数，1，500，000}。
Optical orthogonal signature pattern codes (OOSPCs) play an important role in a novel type of optical code-division multiple-access network for 2-dimensional image transmission. There is a one-to-one correspondence between an -OOSPC and a -(mn, w, 1) packing design admitting an automorphism group isomorphic to . In 2010, Sawa gave a construction of an (m, n, 4, 2)-OOSPC from a one-factor of Kohler graph of which contains a unique element of order 2. In this paper, we study the existence of one-factor of Kohler graph of having three elements of order 2. It is proved that there is a one-factor in the Kohler graph of relative to the Sylow 2-subgroup if there is an S-cyclic Steiner quadruple system of order 2p, where is a prime and . Using this one-factor, we construct a strictly -invariant regular relative to the Sylow 2-subgroup. By using the known S-cyclic SQS(2p) and a recursive construction for strictly -invariant regular G-designs, we construct more strictly -invariant 3-(mn, 4, 1) packing designs. Consequently, there is an optimal -OOSPC for any with and an optimal (6m, 6n, 4, 2)-OOSPC where m, n are odd integers whose all prime divisors from the set is a prime, 1,500,000}.