二次置换多项式 QPP
We also discuss the one-to-one correspondence of orthomorphic permutations and orthomorphic permutation polynomials, and show that for any integer m=2, ax3+bx2+cx+d(a? 0) is not an orthomorphic permutation polynomial of GF(2m), according to the theory of permutation polynomials.
另外，还讨论了正形置换和正形置换多项式具有的一一对应关系，并利用置换多项式的有关理论说明了对任意整数m≥2，ax3+bx2+cx+d（α≠0）不是GF（2m）上的正形置换多项式。
参考来源 - 正形置换的研究与构造·2,447,543篇论文数据，部分数据来源于NoteExpress
与在向量空间上构造的方法比，有限域上置换多项式的代数次数等性质更容易研究。
Compared to the construction over vector space, it is easier to study the properties of permutation polynomials, like algebraic degree.
因此，有限域上的置换多项式一直是一个重要的研究课题，关于这一课题的研究至少有140年的历史。
Hence the research on permutation polynomials has been an important subject for at least 140 years, especially from 70s of the last century for the necessary of the study of cryptography.
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