正形置换的一种新构造与计数  

On the construction and enumeration of orthomorphic permutations

作　　者：廖大见[1,2] 唐元生[1] 

机构地区：[1]扬州大学数学科学院,江苏扬州225002 [2]淮海工学院理学院,江苏连云港222005

出　　处：《通信学报》2010年第S1期70-75,共6页Journal on Communications

基　　金：国家自然科学基金资助项目(60473018)~~

摘　　要：基于正形置换与正形拉丁方截集之间的一一对应关系,研究正形置换的构造,给出n元正形置换之间的一个等价关系,由此在n元正形置换集合内划分等价类,在等价类范围内构造更多的复合截集,并提出基于n元正形置换构造n+1元正形置换的新方法。这个方法更适合于工程实现,且更便于计数,并得到了更多的n+1元正形置换。Based on the one to one corresponding relationship between orthomorphic permutations and transversal of Latin square,the construction issue for orthomorphic permutations was studied.A new equivalent relation between or-thomorphic permutations was proposed.According to the equivalent relation,all the n-bit orthomorphic permutations could be divided into a number of equivalence classes.composite transversal can be constructed could be between these equivalent orthomorphic permutations within an equivalence class.Based on these composite transversal,a new con-struction method was proposed to construct a(n+1) bit orthomorphic permutation from a n-bit one.By this method,enu-meration and counting of orthomorphic permutations are easier and more orthomorphic permutations can be constructed Could be constucted.The method is also easily realized in engineering.

关 键 词：密码学 正形置换 正形拉丁方 截集 

分 类 号：TN918.1[电子电信—通信与信息系统]