A (v. k ) optical orthogonal code (OOC), or briefly a( 1)-OOC,, is a family of (0 1) sequences of length and weight atisfying the following two properties: (1)∑0 tv-1χ1χt+i+for anyχ=(χ0, χ,……，χv-1) ΞC. and any integer 0 (mod ); (1)∑0tv-1χ1χt+i+for anyχ=(χ0, χ,……，for any= with = , and any integer, where the subscripts are reduced modulo. A (v. k )-OOC is optimal if it contains (v. k ) (v. k ) codewords. In this note, we establish that there exists an optimal (3 5 5 1)-OOC for any nonnegative integer whenever is a product of primes congruent to 1 modulo 4. This improves the known existence results concerning optimal OOCs.