Multilength Optical Orthogonal Codes: New Upper Bounds and Optimal Constructions.

Let N=\n0, n1, \ldots , nk-1\ be a set of positive integers and M= \m0, m1, \ldots , mk-1\ be a multiset of positive integers. By an (N, M, w,1; \lambda ) -multilength optical orthogonal code (MLOOC), we mean an MLOOC of autocross correlation value and intracross correlation value one and intercross correlation value \lambda . The code contains mi codewords of weight w and length ni for $0\le i\le k-1$ . The study of MLOOCs is motivated by an application in optical networks requiring multiple signaling rates and quality-of-services. In this paper, we study $(N, M, w,1; \lambda )$ -MLOOCs with $\lambda =2$ (the least value among the nontrivial intercross correlations). Some new upper bounds on code size are derived under certain restrictions and a novel encoding approach is established. A number of series of new MLOOCs are then produced. These codes are of optimal sizes with respect to the new bounds. [ABSTRACT FROM AUTHOR]