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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 + 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.

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Cite

BibTeXRIS
BibTeX
@misc{garg2026classes,
  title = {{New classes of trace-form permutation polynomials and their compositional inverses}},
  author = {Kirpa Garg},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01350},
  eprint = {2609.01350},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01350},
}
RIS
TY  - UNPB
TI  - New classes of trace-form permutation polynomials and their compositional inverses
AU  - Kirpa Garg
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.01350
UR  - https://arxiv.org/abs/2609.01350
AB  - 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.
ER  -