A New Class of Optimal Optical Orthogonal Codes With Weight Five

Abstract

A (v,k,1) optical orthogonal code (OOC), or briefly a (v, k, 1)-OOC, C, is a family of (0,1) sequences of length v and weight k satisfying the following two properties: 1) /spl Sigma//sub 0/spl les/t/spl les/v-1/x/sub t/x/sub t+i//spl les/1 for any x=(x/sub 0/x/sub 1/,...,x/sub v-1/)/spl isin/C and any integer i/spl ne/0 (mod v); 2) /spl Sigma//sub 0/spl les/t/spl les/v-1/x/sub t/y/sub t+i//spl les/1 for any x=(x/sub 0/x/sub 1/,...,x/sub v-1/)/spl isin/C, y=(y/sub 0/y/sub 1/,...,y/sub v-1/)/spl isin/C with x/spl ne/y, and any integer i, where the subscripts are reduced modulo v. A (v, k,1)-OOC is optimal if it contains /spl lfloor/(v-1)/k(k-1)/spl rfloor/ codewords. In this note, we establish that there exists an optimal (3/sup s/5v, 5,1)-OOC for any nonnegative integer s whenever visa product of primes congruent to 1 modulo 4. This improves the known existence results concerning optimal OOCs.