Two Classes Of Optimal Optical Orthogonal Codes Of Weight 4

An optical orthogonal codes is a family of sequence with good auto-correlation and cross-correlation and are widely used in code-division multiple access systems（CDMA）.When the auto-correlation coefficient _aland the cross-correlation coefficient _clare equal,the capacity and construction of optical orthogonal codes have been studied by many scholars.But whenl_a≠l_c,a larger capacity optical orthogonal code can be constructed.From the view of practical application,the larger the capacity of the optical orthogonal code,the more users can be used at the same time,so it has better application value.One-dimensional optical orthogonal codes and two-dimensional optical orthogonal codes are sets of some（0,1）-sequences and（0,1）-matrices respectively,the codewords themselves satisfy the auto-correlation condition,and the codewords satisfy the cross-correlation condition.This paper mainly studies the two types of optimal optical orthogonal codes with Hamming weight of 4 whenl_a≠l_c.First,in Section 1,the current research status and basic concepts of optical orthogonal codes are briefly introduced,and the main results obtained in this paper are briefly described.Section 2 studies the capacity of one-dimensional optical orthogonal codes with autocorrelation coefficients and cross-correlation coefficients of 1 and 2,respectively.According to the number of times the 3-subset orbits appear in the codeword,the upper bound of the one-dimensional（m,4,1,2）optical orthogonal code is given,and the necessary conditions for the existence of the optimal（m,4,1,2）optical orthogonal code and the optimal construction under some parameters are given.Section 3 studies the capacity of two-dimensional（n′m,4,2,1）optical orthogonal codes.Through the relationship between codeword form and support set,the upper bound of two-dimensional（n′m,4,2,1）optical orthogonal codes for the case mo2（mod4）.Finally,through direct construction and recursive construction,the construction of the optimal two-dimensional（n′m,4,2,1）optical orthogonal code with some parameters is given.In the last,the full text is summarized and the future research work is prospected.