| Optical orthogonal codes are commonly used as signature codes for optical code-division multiple access?OCDMA?systems.An optical orthogonal code is a family of sequences with good auto-correlation and cross-correlation properties.The code-division multiple access?CDMA?technique has been successfully used in satellite com-munication and mobile communication field.But due to the limitation of bandwidth,CDMA technique can't express its feature greatly.The optical code-division multiple access system had solved this problem by combining the bandwidth resource with CD-MA technology.In order to further improve CDMA system performance,G.C.Yang proposed the concept of two-dimensional optical orthogonal code?2-D OOC?.A two-dimensional?n ×m,k,?a,?c?optical orthogonal code?briefly 2-D?n ×m,k,?a,?c?-OOC?,C,is a family of n ×m?0,1?-matrices?called codewords?of Ham-ming weight k satisfying the following two properties:?1?the autocorrelation property:for each matrix A =(aij)n×m? C and each integer r,r???0?mod m?,???aijai,j+r??a;?2?the cross-correlation property:for each matrix A =(aij)n×m ? C,B =?bij?n×xm ?C with A ? B,and each integer r,???aijbi,j+r??c,where the arithmetic j + r is reduced modulo m.This paper focuses on optimal two-dimensional optical orthogonal codes with the auto-correlation ?a and the best cross-correlation 1.By examining the structures of w-cyclic group divisible designs and semi-cyclic incomplete holey group divisible designs,we present new combinatorial constructions for two-dimensional?n×m,k,?a,1?-optical orthogonal codes.As a result,when k = 3 and ?a = 2,the exact number of codewords of an optimal two-dimensional?n ×m,3,2,1?-optical orthogonal code is determined for any positive integers n and m?2?mod 4?.The organization of this thesis is as follows:In Chapter 1,we gives a brief introduction on the background of CDMA system,the concept of two-dimensional optical orthogonal code and research status of it.In Chapter 2,we need more g-regular 2-D OOCs,which can be derived from semi-cyclic holey group divisible designs.By examining the structures of w-cyclic group divisible designs and semi-cyclic incomplete holey group divisible designs,we present new combinatorial constructions for 2-D?[n:r]× m,k,?a,1?-OOC.In Chapter 3,when n ? {4,5,7,8,11},we are devoted to constructing optimal 2-D?n × m,k,?a,1?-OOC.In Chapter 4,we prove our main result which determines the exact value of ??n x m,3,2,1?and propose the problems of further research. |
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