Constructions Of MLOOCs Of Weight Three

Code division multiple access (CDMA) is one of the attractive multiple-access schemesfor optical networks. Its prospect is immeasurable. It allows simultaneous users to accessthe same optical channel asynchronously with no delay or scheduling. The key technologyof optical CDMA is the design of optical address code. The late1980s, Chung et al [1]proposed the concept of (one-dimensional) optical orthogonal codes (OOCs). Subsequent-ly, OOCs received widespread attention at home and abroad academia. Simply speaking,an OOC is a family of (0,1) sequences with good auto-and cross-correlation properties.Recent years, in order to simultaneously support multimedia services with diferent signal-ing rates and quality-of-service requirements in optical CDMA networks, academics turnedtheir attention from OOCs of the same length codewords to multi-length OOCs (MLOOCs).Roughly speaking, an MLOOC of small correlation values is a highly structured combina-tion of several constant length OOCs.The present thesis focuses on the problem regarding combinatorial encoding MLOOCsof weight three and enough small correlation values. It is divided into four chapters. Chapter1presents our research background and related concepts. Chapter2presents the equiva-lence between MLOOcs and set systems of compatible cyclic diference packings. The mainresults of this thesis are given in chapters3-4. In chapter3, we establish a number of ap-proaches of constructing MLOOC of weight three§by means of set systems of compatiblecyclic packings. By applying obtained approaches, Chapter4constructs some infinite seriesof MLOOCs of weight3. Their sizes attain or close to the upper bound obtained directlyfrom Johnson bound.