Enumeration of generalized linear orthomorphism in the vector space F q n
Haiqing Han, Qin Li, Yan Tong, Xiusheng Liu · Wuhan University Journal of Natural Sciences · 2012
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.