The Combinatorial Constructions For Variable-weight Optical Orthogonal Codes

In 1989,optical orthogonal code was introduced by Salehi,as signature sequences to facilitate optical code division multiple access(OCDMA)system.Variable-weight optical orthogonal code was introduced by Yang for multimedia OCDMA systems with multiple quality of service(QoS)requirement.Let W,L,and Q denote the sets{w0,w1,…,wp},{λa0,λa1,…,λap}and{q0,q1,…,qp}, respectively as defined below.Without loss of generality,we assume that w018.Theorem 1.6 There exists an optimal(u,{3,4},1,{1/2,1/2})-OOC for any integer u≡9(mod 18),and u>9.Theorem 1.7 There exists an optimal(u,{3,5},1,{1/2,1/2})-OOC for any integer u≡13(mod 26),and u>13.Theorem 1.8 There exists an optimal(ν,{3,6},1,{1/2,1/2})-OOC for any positive integerν≡2(mod 36),andν/2 is a prime.Theorem 1.9 There exists an optimal(ν,{3,6},1,{1/2,1/2})-OOC for any positive integerν≡42,186(mod 216),andν/6 is a prime.Theorem 1.10 There exists an optimal(ν,{4,5},1,{1/2,1/2})-OOC for any positive integerν≡40(mod 64),ν/8 is a prime,andν>40.The paper is divided into five parts. In chapter one,we present some notations,the known results on(variable-weight)optical orthogonal codes and the main results of this pa-per.Chapter two discusses the existence of optimal(ν,{3,4},1,{1/2,1/2})-OOCs.Chapter three discusses the existence of(ν,{3,5},1,{1/2,1/2})-OOCs.Chapter four talks about the existence of(ν,{3,5},1,{1/2,1/2})-OOCs.Further research problems are given in Chapter five.