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This is a Quantitative Study study.

October 15, 2025International Journal of Foundations of Computer Science

A new class of permutation quadrinomial over 𝔽q2 with characteristic 5

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The quadrinomial demonstrates properties of permutation polynomials for certain conditions on its coefficients.
Finding conditions for permutation quadrinomial is contingent upon the parity of the parameters involved.
The study employs a detailed analysis within the framework of finite fields to clarify operation limits.
Understanding permutation polynomials can have implications in areas like coding theory and cryptography.

Implication

This analysis identifies permutation polynomials in finite fields using specific quadrinomial forms.

Abstract

Let [Formula: see text], [Formula: see text] be a natural number, [Formula: see text] the finite field of order [Formula: see text], and [Formula: see text]. In this paper, we find that the quadrinomial [Formula: see text] is a permutation polynomial if [Formula: see text] is a positive integer for [Formula: see text]; [Formula: see text] is odd for [Formula: see text] and [Formula: see text] is even for [Formula: see text]. We also find that [Formula: see text] is a permutation quadrinomial over [Formula: see text].

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Cite This Study

Wang et al. (2025) studied this question.

synapsesocial.com/papers/68ef858cc6a308ba06355429 https://doi.org/10.1142/s0129054125500376

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Implication

This analysis identifies permutation polynomials in finite fields using specific quadrinomial forms.

A new class of permutation quadrinomial over 𝔽q2 with characteristic 5

Key Points

Implication

Abstract

Discussion

Cite This Study

A new class of permutation quadrinomial over 𝔽q2 with characteristic 5

Key Points

Implication

Abstract

Discussion

Cite This Study