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Sparse Lifts of q-Linearized Permutation Polynomials with Explicit Inverses
Abstract
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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BibTeX
@misc{li2026sparse,
title = {{Sparse Lifts of q-Linearized Permutation Polynomials with Explicit Inverses}},
author = {Yi Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16619},
eprint = {2610.16619},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16619},
}
RIS
TY - UNPB
TI - Sparse Lifts of q-Linearized Permutation Polynomials with Explicit Inverses
AU - Yi Li
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16619
UR - https://arxiv.org/abs/2610.16619
AB - 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.
ER -