A Class Of The Optimal Two-dimentional Optical Orthogonal Codes

An optical orthogonal code is a family of sequences with good auto-correlation andcross-correlation properties. It is used to be a special code for optical code-divisionmultiple access(CDMA) systems. The code-division multiple access(CDMA) techniquehas been successfully used in satellite communication and mobile communication field,but due to the limitation of bandwidth, the advantages of CDMA technique can not playadequately. The optical code-division multiple access system had solved this problem bycombining the bandwidth resource with CDMA technology. In an optical code-divisionmultiple access system, different users can be identified by the only spread spectrumsequence. Each user′s data is extended through their spread spectrum sequence, andthen all the users are coupled to the shared channel. The optical orthogonal codes issuch a family of sequences with good auto-correlation and cross-correlation properties,and therefore it is more suitable to be the spread-spectrum sequence in the optical codedivision multiple access system.A two-dimensional optical orthogonal code is a family of(0, 1) matrices with goodauto-correlation and cross-correlation properties. And an optimal two-dimensional opti-cal orthogonal code is such a two-dimensional optical orthogonal codes with the largestnumber of codewords.In this paper, we will compute the formula of the number of the codewords for theoptimal two-dimensional optical orthogonal code with weight k, λa= k- 2 and λc= k- 1.And then we give the exact value for the case k = 5.