Enumeration of Generalized Linear Orthomorphism in the Vector Space F_q^n

作     者：HAN Haiqing LI Qin TONG Yan LIU Xiusheng 

作者机构：. School of Mathematics and Physics Huangshi Institute ofTechnology Huangshi 435003 Hubei China Department of Normal Huangshi Institute of TechnologyHuangshi 435003 Hubei China . School of Computer Wuhan University Wuhan 430072Hubei China 

出 版 物：《Wuhan University Journal of Natural Sciences》 (武汉大学学报（自然科学英文版）)

年 卷 期：2012年第17卷第1期

页      面：43-47页

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 08[工学] 

基　　金：Supported by the National Natural Science Foundation of China (60970115  91018008) 

主　　题：block cipher P-permutation generalized linear orthomorphism the branch number counting formula 

摘      要：The conception of orthomorphism has been generalized in this paper, and a counting formula on the generalized linear orthomorphism in the vector space over the Galois field with the arbitrary prime number p as the characteristic is obtained. Thus, the partial generation algorithm of generalized linear orthomorphism is achieved. The counting formula of the linear orthomorphism in the vector space over the finite field with characteristic 2 is the special case in our results. Furthermore, the generalized linear orthomorphism generated and discussed in this paper can gain the maximum branch number when they are designed as P-permutations.