Further results on optimal -OOCs for

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 ( mod 26 ) , and v ≥ 39 . It is also shown that an optimal ( 2 u , { 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.