Further results on optimal (v,{3,k},1,{1/2,1/2})-OOCs for k=4,5

Variable-weight optical orthogonal code (OOC) was introduced by Yang for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. Some results on the existence of optimal (v,{3,k},1,{1/2,1/2})-OOCs for k=4,5 were obtained. In this paper, it is proved that there exists an optimal (v,{3,5},1,{1/2,1/2})-OOC for each positive integer v≡13(mod26), and v≥39. It is also shown that an optimal (2u,{3,4},1,{1/2,1/2})-OOC exists for any positive integer u whose prime factors are all congruent to 1 modulo 18 and not less than 19.