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| 几类\mathbb{F}_{2^{3m}}上具有旋转结构置换多项式的构造 |
| Construction of Permutation Polynomials with Rotational Structure over\mathbb{F}_{2^{3m}} |
| 投稿时间：2025-03-24 修订日期：2025-05-08 |
| DOI： |
| 中文关键词: 置换多项式 三变元 有限域 向量空间 |
| 英文关键词:permutation polynomials trivariate form finite fields vector space |
| 基金项目:湖南省自然科学基金面上项目2023JJ30517 |
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| 摘要点击次数: 19 |
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| 中文摘要: |
| 有限域上置换多项式的构造和应用是密码学、编码学和组合学等领域的热点问题。向量空间\mathbb{F}_{2^m}^3上的置换函数与有限域\mathbb{F}_{2^{3m}}上的置换多项式可以相互转化,本文研究了向量空间\mathbb{F}_{2^m}^3上具有旋转结构的置换函数,构造了三类有限域\mathbb{F}_{2^{3m}}上的置换多项式,运用结式法、多变元法、待定系数法以及指数和等方法,从理论上证明了构造的函数具有置换性质。 |
| 英文摘要: |
| Permutation polynomials are hot topics in the fields of cryptography, combinatorics, coding theory and related fields. There exists a correspondence between permutation functions on the vector space \mathbb{F}_{2^m}^3 and permutation polynomials over the finite field \mathbb{F}_{2^{3m}}. In this paper, we investigate permutation functions on \mathbb{F}_{2^m}^3 with rotational structures and construct three classes of permutation polynomials. We prove that they are indeed permutations by constructing a system of equations, primarily using methods such as resultants, multivariate techniques, the method of undetermined coefficients, and exponential sums. |
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