具有显式逆的q线性化置换多项式的稀疏提升
Sparse Lifts of q-Linearized Permutation Polynomials with Explicit Inverses
AI总结：
该研究构造了保持复合逆的q线性化置换多项式的稀疏提升，得到二维二项式、三维三项式等的显式逆，为有限域上置换多项式的构造提供了新方法。
摘要：
我们给出从F_q^n上的q线性化置换多项式到F_q^{ns}上一般非线性稀疏置换多项式的高单位环提升。该构造保持复合逆：若线性化多项式及其逆的系数为(a_i)和(A_i)，则提升后的多项式及其逆具有相同系数。因此，我们得到非线性二项式提升，其逆在二维情形下仍为二项式，包括F_q^4上二项式族的显式逆；三维特例产生置换三项式，其复合逆仍为三项式，附带显式对合准则及实例。
英文摘要：
We give a higher unit-torus lift from q-linearized permutation polynomials over Fqn to generally nonlinear sparse permutation polynomials over Fqns. The construction preserves compositional inverses: if a linearized polynomials and its inverse have coefficients (ai) and (Ai), then the lifted polynomial and its inverse have the same coefficients. As a consequence, we obtain nonlinear binomial lifts whose inverses are again binomials in the two-dimensional case, including an explicit inverse for a binomial family over Fq4. The three dimensional specialization yields permutation trinomials whose compositional inverses are again trinomials, together with explicit involution criteria and examples.
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