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Cryptography and Communications
Erschienen in: Cryptography and Communications 2/2024

19.09.2023 | Research

Some classes of permutation binomials and trinomials of index \(q-1\) over \({\mathbb {F}_{q^n}}\)

verfasst von: Rohit Gupta, Luciane Quoos, Qiang Wang

Erschienen in: Cryptography and Communications | Ausgabe 2/2024

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Abstract

In this paper, using the classification of degree 7 permutations over \(\mathbb {F}_q\), we classify certain sparse PPs of the form \(P(x)=x^rf(x^{\frac{q^n-1}{q-1}})\) of \(\mathbb {F}_{q^n}\) for \(n=2\) and 3. In particular, we give necessary and sufficient conditions for the polynomial \(f_{a,b}(x):=x(x^{2(q^2+q+1)}+ax^{q^2+q+1}+b)\) in \(\mathbb {F}_{q^3}[x]\) to be a permutation polynomial over \(\mathbb {F}_{q^3}\), where \(q >409\) is a prime power.
Vorheriger Artikel A direct construction of optimal 2d-zcacs with flexible array size and large set size
Nächster Artikel A direct construction of complete complementary code with zero correlation zone property for prime-power length

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Metadaten
Titel
Some classes of permutation binomials and trinomials of index over
verfasst von
Rohit Gupta
Luciane Quoos
Qiang Wang
Publikationsdatum
19.09.2023
Verlag
Springer US
Erschienen in
Cryptography and Communications / Ausgabe 2/2024
Print ISSN: 1936-2447
Elektronische ISSN: 1936-2455
DOI
https://doi.org/10.1007/s12095-023-00674-y

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