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Journal of Discrete Mathematical Sciences and Cryptography

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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

Some classes of permutation polynomials of the form x(xs1(q+1) + bxs2(q+1)+a) over Fq2

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pp. 907–930Vol. 28Issue 3April 2025DOI: 10.47974/JDMSC-2192 Crossmark XML
Received:
16 Jan 2024
Published Online:
12 Apr 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2192
Pages:
907–930

Abstract

Permutation polynomials hold significant relevance in the practical applications of finite fields. Presently, they constitute a pivotal focus in contemporary research endeavors. This paper undertakes the classification of permutation binomials and trinomials of the form x(xs1 (q+1)+bs2 (q+1)+a) over Fq2, with s1=3. We explore these polynomials with variations in b, considering the cases where b = 0 or b ≠ 0 with s2 =1 and s2 = 2.

Keywords

Finite fieldsPermutation polynomialPermutation binomialPermutation trinomial

Subject Classifications

11T0611T5505A05

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