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arXiv · 2609.01350

New classes of trace-form permutation polynomials and their compositional inverses

Kirpa Garg
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Abstract

We construct permutation polynomials of the form x + \gamma Tr^{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.

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Kirpa Garg. 2026-09-01. New classes of trace-form permutation polynomials and their compositional inverses. https://arxiv.org/abs/2609.01350

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