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中文摘要：
基于正形置换的定义，给出一个实用的正形置换构造算法及其应用，得到全部16次正形置换的计数为244744192；通过求解有限域F2^m上矩阵的逆矩阵，给出一个简捷的F2^m上与一个置换对应的置换多项式构造方法。得到了有限域F2^4上的全部正形置换多项式。并且证明其多项式次数均小于14．证明了有限域F2^m上置换多项式的多项式次数均小于2^m-1.
英文摘要：
Orthomorphic permutations are important in block ciphers designs. Based on the definition of orthomorphic permutation, a practical method is presented to generate all orthomorphic permutations over F2^m, and it was verified that the number of all orthomoriphic permutations over F2^4 is 244 744 192. By the inverse matrix of a matrix over finite field F2^n, a brief method was presented to generate a permutation polynomial corresponding to every permutation over F2^m, and all orthomotheriphic permutation polynomials over F2^4 were analysed and found to be of order less than 14. It was proved that the order of permutation polynomial over F2^m is less than 2^m- 1.
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