Optical orthogonal codes: their bounds and new optimal constructions

Abstract

A (v, k, /spl lambda//sub a/, /spl lambda//sub c/) optical orthogonal code (OOC) C is a family of (0, 1)-sequences of length v and weight k satisfying the following two correlation properties: (1) /spl Sigma//sub 0/spl les/t/spl les/v-1/x/sub t/x/sub t+i//spl les//spl lambda//sub a/ for any x=(x/sub 0/,x/sub 1/,/spl middot//spl middot//spl middot/,x/sub v-1/)/spl isin/C and any integer i not equivalent 0 mod v; and (2) /spl Sigma//sub 0/spl les/t/spl les/v-1/x/sub t/y/sub t+i//spl les//spl lambda//sub b/ for any x=(x/sub 0/,x/sub 1/,/spl middot//spl middot//spl middot/, x/sub v-1/) /spl isin/ C, y=(y/sub 0/,y/sub 1/,/spl middot//spl middot//spl middot/,y/sub v-1/) /spl isin/C with x/spl ne/y, and any integer i, where the subscripts are taken modulo v. The study of optical orthogonal codes is motivated by an application in optical code-division multiple-access communication systems. In this paper, upper bounds on the size of an optical orthogonal code are discussed. Several new constructions for optimal optical orthogonal codes with weight k/spl ges/4 and correlation constraints /spl lambda//sub a/=/spl lambda//sub c/=1 are described by means of optimal cyclic packings. Many new infinite series of such optimal optical orthogonal codes are thus produced.