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

05.09.2023 | Research

Three classes of permutation quadrinomials in odd characteristic

verfasst von: Changhui Chen, Haibin Kan, Jie Peng, Lijing Zheng, Yanjun Li

Erschienen in: Cryptography and Communications | Ausgabe 2/2024

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Abstract

In this paper, we construct three classes of permutation quadrinomials with Niho exponents of the form \(f(x)=\alpha _0x^r+\alpha _1x^{s_1(p^m-1)+r}+\alpha _2x^{s_2(p^m-1)+r}+\alpha _3x^{s_3(p^m-1)+r}\in \mathbb {F}_{p^{n}}[x]\), where p is an odd prime, \(n=2m \) is a positive even integer, and \((r,s_1,s_2,s_3)=(1,\frac{-1}{p^k-2},1,\frac{p^k-1}{p^k-2})\), \((1,\frac{p^k+1}{p^k+2},1,\frac{1}{p^k+2})\) and (3, 1, 2, 3), respectively. The exponents of the first two classes are considered for the first time, and the third class covers all the permutation polynomials proposed by Gupta (Designs Codes and Cryptography 88, 1–17, 2020).
Vorheriger Artikel The cross-correlation spectrum of ternary perfect sequences and their decimations
Nächster Artikel A direct construction of optimal 2d-zcacs with flexible array size and large set size

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Metadaten
Titel
Three classes of permutation quadrinomials in odd characteristic
verfasst von
Changhui Chen
Haibin Kan
Jie Peng
Lijing Zheng
Yanjun Li
Publikationsdatum
05.09.2023
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/s12095-023-00672-0

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