F_2~n上的正形置换

On Orthomorphisms over F_2~n

讨论了正形置换的构造和性质,并分析了正形置换的幂次是否仍是正形置换.对于线性正形置换,根据矩阵标准型的性质,只要整数i不能被这个正形置换对应矩阵的极小多项式的各个根的阶整除,则这个线性正形置换的i次幂仍是线性正形置换.对于非线性正形置换,给出了有用的结果.

We mainly discuss the constructions and properties of orthomorphisms, and concern whether the power of one orthomorphism is still one orthomorphism. For linear orthomorphism, using the properties of canonical form of matrix, if integer i can＇t be divided exactly by the orders of roots of the minimum polynomial of the matrix corresponding to this orthomorphism, then the i-th power of this linear orthomorphism is still one linear orthomorphism. For nonlinear orthomophisms, we provide some useful results.