(Z_u×Z_v,4,1)差填充及其在光正交签名码中的应用  

(Z_u×Z_v,4,1) Difference Packings and Applications to Optical Orthogonal Signature Pattern Codes

作　　者：赵恒明 覃荣存[2] ZHAO Hengming;QIN Rongcun(School of Mathematics and Information Science,Guangxi College of Education,Nanning,Guangxi,530023,P.R.China;Xingjian College of Science and Liberal Arts,Guangxi University,Nanning,Guangxi,530005,P.R.China)

机构地区：[1]广西教育学院数学与信息科学学院,南宁广西530023 [2]广西大学行健文理学院,南宁广西530005

出　　处：《数学进展》2020年第5期528-548,共21页Advances in Mathematics（China）

基　　金：Supported by Guangxi Science Foundation (No.2018GXNSFBA138038,2019GXNSFBA245021);Bagui Scholar Program of Guangxi Zhuang Autonomous Region of China (No.201979);the Research Foundation of Guangxi University Xingjian College of Science and Liberal Arts (No.Y2018ZKT01)。

摘　　要：为了解决二维图像的并行传输,北山研一引入了光正交签名码.在光正交签名码的研究中,(Zu×Zv,k,1)差填充起到重要的作用.本文给出了群Z3×Zgp上(3×gp,3×g,4,1)-DF和群Z3p×Zgp上(3p×gp,3×g,4,1)-DF的具体构造,其中g=3,6,从而通过递推构造给出若干类最优(Zu×Zv,4,1)差填充.因此,我们得到若干类重量为4的光正交签名码.Optical orthogonal signature pattern codes(OOSPCs) were introduced by Kitayama for parallel transmission of two-dimensional images.In a study of optical orthogonal signature pattern codes,(Zu×Zv,k,1) difference packings play an important role.In this paper,explicit constructions for a(3 × gp,3 ×g,4,1)-DF over Z3 × and a(3 p × gp,3 ×g,4,1)-DF over Z3 p×Zgp are presented,where g=3,6,so we obtain some series of optimal(Zu × Zv,4,1)difference packings via recursive constructions.Consequently,some infinite classes of optimal optical orthogonal signature pattern codes with weight 4 are obtained.

关 键 词：差填充 光正交签名码 相对差族 

分 类 号：O157.2[理学—数学]