The Combinatorial Constructions Of Optimal Optical Orthogonal Codes With Weight Five

Along with the fast development of science and technology, the requirement of network is increasing and the industry of electronic information develops so quickly, which lead to strictly demands for the capacity of the net and webwidth.Optical code division multiple access (OCDMA) communication technology is the com-bination of code division multiple access (CDMA) communication technology and fiber optic communication technology with high capacity. It has the characteristic features of both two communication technologies at the same time. Among the address codes of OCDMA, optical orthogonal code (OOC) is a better one. Compared with others, OOC has smaller weight and good correlation properties. Accordingly, OOC is concerned much more by scholars at home and abroad. It becomes more important.Because of the close relationship between the optimal OOCs and the theory of combina-torial designs, we can discuss the existence of relative cyclic packing designs instead of the existence of OOCs. However, cyclic design is one of the fundamental problems of the theory of combinatorial designs.In this paper, we obtain the existence of a g-regular CP(5,1; gp) by applying the theory of cyclotomic domain to direct and recursive constructions with some g∈{2,9,10,12,14,20} af-ter surveying the background. It is divided into three parts. In the first part, we mainly introduce the definition of OOC. Then we list the known results and the main conclusions of this paper. In the second part, we introduce the theory of cyclotomic domain and Weil’s Theorem. Then we obtain the existence of a g-regular CP(5,1; gp) by direct constructions with g∈{2,9,12,20}. In the third part, we get more conclusions by recursive constructions through cyclic difference matrix.