论文标题
具有系数1的新类排列多项式在有限场上
New classes of permutation polynomials with coefficients 1 over finite fields
论文作者
论文摘要
具有系数1的置换多项式在有限场上，由于简单的代数形式吸引了研究人员的兴趣。在本文中，我们首先在$ \ mathbb {f} _ {2^{2M}} $的循环子组上构造了四类分数置换多项式。从这些置换的多项式中，构建了三个新的置换多项式多项式，构建了系数1，具有系数1，构建了$ \ mathbb {f} _ {2^{2m}} $，而又有三个一般的置换多项式的新型置换式多项式的系数为$ \ mathbb {f} _ {f} = 2m} $ new of $ \ mathbb {2m} $ new ofer new quester。一些已知的置换多项式是我们新置换多项式的特殊情况。此外，我们证明，在所有新的置换多项式中，存在一个置换多项式，该置换符合所有正面整数$ m $的已知排列多项式。此证明表明，可以通过$ \ \ mathbb {f} _ {q} $的环环子组上的ea-nimenequivalent置换多项式多项式{f} _ {q} $。从这个证据来看，很明显，在所有新的置换多项式中，存在一个置换多项式，其中代数度是$ \ mathbb {f} _ {2^{2m}} $的最大代数置换多项式多项式多项式。
Permutation polynomials with coefficients 1 over finite fields attract researchers' interests due to their simple algebraic form. In this paper, we first construct four classes of fractional permutation polynomials over the cyclic subgroup of $ \mathbb{F}_{2^{2m}} $. From these permutation polynomials, three new classes of permutation polynomials with coefficients 1 over $ \mathbb{F}_{2^{2m}} $ are constructed, and three more general new classes of permutation polynomials with coefficients 1 over $ \mathbb{F}_{2^{2m}} $ are constructed using a new method we presented recently. Some known permutation polynomials are the special cases of our new permutation polynomials. Furthermore, we prove that, in all new permutation polynomials, there exists a permutation polynomial which is EA-inequivalent to known permutation polynomials for all even positive integer $ m $. This proof shows that EA-inequivalent permutation polynomials over $ \mathbb{F}_{q} $ can be constructed from EA-equivalent permutation polynomials over the cyclic subgroup of $ \mathbb{F}_{q} $. From this proof, it is obvious that, in all new permutation polynomials, there exists a permutation polynomial of which algebraic degree is the maximum algebraic degree of permutation polynomials over $ \mathbb{F}_{2^{2m}} $.
