模2^n剩余类环上的多项式变换的研究

Researches on polynomial transformation over residue classes ring modulo 2^n

对模2n剩余类环上的多项式变换进行了详细的研究和分析。给出了模2n剩余类环上的m(m≥1)次多项式变换是置换的一个充分必要条件;给出了模2n剩余类环上的m(m≥1)次置换多项式个数的一个上界。

Polynomial transformation over residue classes ring modulo 2^n is researched deeply in this paper.Let f be a polynomial transformation over residue classes ring modulo 2^n of degree m,a sufficiency and necessity condition such that f is a permutation is given.Upper bounds for the number of permutation polynomials over residue classes ring modulo 2^n of degree m is also given.