A new class of optimal optical orthogonal codes with weight five

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) Σ_0≤t≤v-1x_tx_t+i≤1 for any x=(x₀x₁,...,x_v-1)∈C and any integer i≠0 (mod v); 2) Σ_0≤t≤v-1x_ty_t+i≤1 for any x=(x₀x₁,...,x_v-1)∈C, y=(y₀y₁,...,y_v-1)∈C with x≠y, and any integer i, where the subscripts are reduced modulo v. A (v, k,1)-OOC is optimal if it contains └(v-1)/k(k-1)┘ codewords. In this note, we establish that there exists an optimal (3^s5v, 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.