On optimal (v,5,2,1) optical orthogonal codes

The size of a (v, 5, 2, 1) optical orthogonal code (OOC) is shown to be at most equal to ⌈ v/12⌉ when v ≡ 11 (mod 132) or v ≡ 154 (mod 924), and at most equal to ⌊v/12⌋ in all the other cases. Thus a (v, 5, 2, 1)-OOC is naturally said to be optimal when its size reaches the above bound. Many direct and recursive constructions for infinite classes of optimal (v, 5, 2, 1)-OOCs are presented giving, in particular, a very strong indication about the existence of an optimal (p, 5, 2, 1)-OOC for every prime p ≡ 1 (mod 12).