New results on optimal \((v,4,2,1)\) optical orthogonal codes (Q629878)

This paper considers optimal \((v, 4, 2, 1)\) optical orthogonal codes (OOC), where optimal means that the size of the code is \(\lceil \frac{v}{8}\rceil\) or \(\lfloor \frac{v}{8}\rfloor\). It proves that there is no optimal \((v,4,2,1)\)-OOC when \(v \equiv 24, 33 \pmod{72}\), or \(v \equiv 42, 48, 51, 57 \pmod{72}\) with \(v \not\equiv 0 \pmod{7}\). Several infinite classes of optimal \((v, 4, 2, 1)\)-OOC are also constructed, which have some extra combinatorial property.