新型迹形式置换多项式及其复合逆
New classes of trace-form permutation polynomials and their compositional inverses
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中文总结 AI 辅助
该研究在有限域F_{q^2}上构造两类系数覆盖全域的迹形式置换多项式，计算其复合逆，所用Kloosterman和与有限域方程分析技术具独立研究价值。
中文摘要 AI 辅助
我们在有限域F_{q^2}上构造形如x + γ Tr^{q^2}_q(h(x))的置换多项式。更确切地说，我们提出两类系数覆盖域中所有元素而非局限于真子域的置换多项式族，并计算这两类族的复合逆。我们的技术涉及特定Kloosterman和的计算以及有限域上某些方程的分析，且认为这些技术具有独立研究价值。
英文摘要
We construct permutation polynomials of the form x + γTr^{q^2}_q(h(x)) over the finite field F_{q^2}. More precisely, we present two families ofpermutation polynomials whose coefficients range over all elements of the field rather than being restricted to a proper subfield. We also compute the compositional inverses of both families. Our techniques involve the evaluation of certain Kloosterman sums together with the analysis of some equations over finite fields, and we believe these can be of independent interest.
发表机构
- University of Rouen Normandy（诺曼底鲁昂大学）
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