| In 1989,one-dimensional constant-weight optical orthogonal code(1D CWOOC)was introduced by Salehi.It was applied in optical code division multiple access(OCDMA)system as a signature sequence.Yang introduced one-dimensional variable-weight optical orthogonal code(1D VWOOC)in 1996 to meet multiple QoS requirements.With the rapid development of the society and the requirement for different forms of information are im-proved,people need OCDMA with high speed,large capacity and different bit error rate.In order to expand the capacity of OOC,two-dimensional constant-weight optical orthogonal code(2D CWOOC)was introduced by Yang in 1997,similar to 1D CWOOC.2D CWOOC can not meet QoS requirements too.To solve the problem,two-dimensional variable-weight optical orthogonal code(2D VWOOC)was introduced.The definition of 2D VWOOC will be given bellow.Let W = {w1,...,wr} be an ordering of a set of ? integers greater than 1,?a=(?a(1),...,?a(r))an r-tuple of positive integers,and Q =[q1,...,qr)an r-tuple of positive rational numbers whose sum is 1.Without loss of generality,we assume that w1<w2<...<wr.An(u×v,W,?a,?c,Q)variable-weight optical oithogoual code or(u×v,W,?a,?c,Q)-OOC C,is a collection of(0,1)u×v matrices(codewords)such that the following three properties hold:(1)Weight Distribution:The ratio of codewords of C with Hamming weight wk is qk,1?k?r;(2)Periodic Auto-correlation:For 0<?<v-1,and matrix X in C with Hamming weight wk,where(?)(?)(3)Periodic Cross-correlation:For 0??<v-1 and any two distinct matrices X.Y in C.wherewhere ? denote modulo v addition.If an OOC has maximum code size,it is said to be optimal.For optinnal(v,W,l,Q)-OOCs,many results had been done,while not so much had been done on optimal 2D VWOOCs.In this thesis,the following results are obtained:Theorem 1.1 If there is a skew starter in Zv,then there exist a 1-regular and an optimal(6×v,{3.4},1,(4/5,1/5))-OOC.Theorem 1.2 If there is a skew starter in Zv,then there exists a 1-regular(6 × v.{3,4},1,(2/3,1/3))-OOC.Theorem 1.3 If there is a skew starter in Zv,then there exists a 1-regular(9 × v.{3.4},1,(7/8.1/8))-OOC.Theorem 1.4 let v be positive integer,if each prime factors p of v all satisfy p ? 1(mod 4),then there exist,a.1-regular and an optimal(3 × v.{3.4},1.(4/5.1/5))-OOC.Theorem 1.5 let v be a positive integer,if each prime factors p of v are all satisfy p ? 1(mod 4),then there exist a 1-regular and an optimal(6×v,{3.4},1,(6/7.1/7))-OOC.Theorem 1.6 let v be a positive integer,if each prime factors p of v are all satisfy p?1(mod 4),then there exist a 1-regular and an optimal(G × v.{3.4}.1.(10/11.1/11))-OOC.Theorem 1.7 let v be a positive integer,if each prime factors p of v are all satisfy p ? 1(mod 4),then there exist a.1-regular and an optimal(3 × v,{3.4}.1,(22/23.1/23))-OOC.Theorem 1.8 let v be a positive integer.if each prime factors p of v are all satisfy p ? 1(mod 6),then there exist a 1-regular and an optimal(3×v {3.4},1,(1/2.1/2))-OOC.Theorem 1.9 let v be a positive integer,if each prime factors p of v are all satisfy p ? 1(mod 6),then there exist a 1-regular and an optimal(3×v,{3,4},1,(2/5,3/5))-OOC.Theorem 1.10 let v be a positive integer,if each prime factors p of v are all satisfy p ? 1(mod 6),then there exist a 1-regular and an optimal(4×v,{3,4},1,(6/7,1/7))-OOC.Theorem 1.11 let v be a positive integer,if each prime factors p of v are all satisfy p ? 1(mod 6),then there exist a 1-regular and an optimal(4 × v,{3,4},1,(10/13,3/13))-OOC.Theorem 1.12 let v be a positive integer,if each prime factors p of v are all satisfy p ? 1(mod 6),then there exist a 1-regular and an optimal(6 × v,{3,4},1,(3/4,1/4))-OOC.Theorem 1.13 let v be a positive integer,if each prime factors p of v are all satisfy p ? 1(mod 6),then there exist a 1-regular and an optimal(5 × v,{3,4},1,(19/22,3/22))-OOC.Theorem 1.14 let v be a positive integer,if each prime factors p of v are all satisfy p?7(mod 12),p>31,then there exist a 1-regular and an optimal(4×v {3,4},1,(6/11,5/11))-OOC.Theorem 1.15 let v be a positive integer,if each prime factors p of v arc all satisfy p ?1(mod 4),then there exist a 1-regular and an optimal(5×v {3,4,5},1,(3/5,1/5,1/5))-OOC.Theorem 1.16 If there is a skew starter in Zv,then there exist a 1-regular and an optimal(7×v,{3,4},1,(7/11,3/11,1/11))-OOC.There are four parts in these thesis.In Chapter one,some notations and the main results are presented.In chapter two we give the construction of optimal(u×v,{3.4},1,Q)-OOCs.In chapter three we give the construction of optimal(u × u,{3,4.5},1,Q)-OOCs.Conclusions and further research problems are presented in Chapter four. |
PDF Full Text Request