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PreprintCC BY 4.0arXiv

On some Non-Permutations of Quadratic Extension of Finite Field

  • Bidushi Sharma
  • Dhiren Kumar Basnet
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Abstract

In this article, we study polynomials over 𝔽q2 that do not permute 𝔽q2. More precisely, we characterize polynomials of the forms xq + b x2 + c x + d and xq+1 + b xq + c x + d over 𝔽q2 according to whether they are permutation or non-permutation polynomials. To this end, we determine the exact number of zeros of these polynomials using existing results on certain special Weil sums.

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Cite

BibTeXRIS
BibTeX
@misc{sharma2026some,
  title = {{On some Non-Permutations of Quadratic Extension of Finite Field}},
  author = {Bidushi Sharma and Dhiren Kumar Basnet},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.14529},
  eprint = {2606.14529},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.14529},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On some Non-Permutations of Quadratic Extension of Finite Field
AU  - Bidushi Sharma
AU  - Dhiren Kumar Basnet
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2606.14529
UR  - https://arxiv.org/abs/2606.14529
AB  - In this article, we study polynomials over 𝔽_q^2 that do not permute 𝔽_q^2. More precisely, we characterize polynomials of the forms x^q + b x^2 + c x + d and x^q+1 + b x^q + c x + d over 𝔽_q^2 according to whether they are permutation or non-permutation polynomials. To this end, we determine the exact number of zeros of these polynomials using existing results on certain special Weil sums.
ER  -