Permutation polynomials with a few terms over finite fields

This paper considers permutation polynomials over the finite field $ \mathbb F_{q^2} $ by utilizing low-degree permutation rational functions over $ \mathbb F_q $, where $ q $ is a prime power. As a result, we obtain two classes of permutation binomials, six classes of permutation quadrinomials and six classes of permutation pentanomials over $ \mathbb F_{q^2} $. Additionally, we show that the obtained binomials, quadrinomials and pentanomials are quasi-multiplicative inequivalent to the known ones in the literature.

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Publication Details

Journal
Advances in Mathematics of Communications
Published
2025-08-26
DOI
https://doi.org/10.3934/amc.2025040
Primary Topic
Coding theory and cryptography
Type
article
Field-Weighted Citation Impact
0.00

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article

Permutation polynomials with a few terms over finite fields

Kirpa Garg, Sartaj Ul Hasan, Mohit Pal, Harish Kumar et al.
Advances in Mathematics of Communications
Coding theory and cryptography
article

Permutation polynomials with a few terms over finite fields

Kirpa Garg, Sartaj Ul Hasan, Mohit Pal, Harish Kumar, Chunlei Li
article en

Abstract

This paper considers permutation polynomials over the finite field $ \mathbb F_{q^2} $ by utilizing low-degree permutation rational functions over $ \mathbb F_q $, where $ q $ is a prime power. As a result, we obtain two classes of permutation binomials, six classes of permutation quadrinomials and six classes of permutation pentanomials over $ \mathbb F_{q^2} $. Additionally, we show that the obtained binomials, quadrinomials and pentanomials are quasi-multiplicative inequivalent to the known ones in the literature.

Advances in Mathematics of CommunicationsVol. 21(0)
Indian Institute of Technology Jammu (IN), University of Bergen (NO)
Norges Forskningsråd, Science and Engineering Research Board
Openalex Percentile: Top 88%
Coding theory and cryptography
DOIOpen Access PDFOpenAlex
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Permutation polynomials with a few terms over finite fields — Kirpa Garg, Sartaj Ul Hasan, et al. · Advances in Mathematics of Communications (2025) | TGRS Research Map | TGRS