Generalized Linear Orthomorphisms
Qin Li, Kang Shi, Haiqing Han, Siru Zhu, Yanqing Dai, Qili Mao · International Journal of Reasoning-based Intelligent Systems · 2020
In this study, we generalize the conception of orthomorphisms and obtain a counting formula on the generalized linear orthomorphisms over the Galois field with the arbitrary prime number p as the characteristic. Thus the partial generation algorithm of generalized linear orthomorphisms is achieved. The counting formula of the linear orthomorphisms over the finite field with characteristic 2 is the special case in our results. Furthermore, the generalized linear orthomorphisms generated and discussed in this study can gain the maximum branch number when they are designed as P-permutations.