A revisit to a class of permutation quadrinomials

This paper revisits the quadrinomials x3q+a1x2q+1+a2xq+2+a3x3 over Fq2, where q is a power of 2. We propose a more comprehensive characterization of the coefficients that give rise to new permutation quadrinomials. The new characterization not only contains those coefficients given in [20], but also...

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Bibliographic Details
Published in:Finite fields and their applications 2019-09, Vol.59, p.57-85
Main Authors: Tu, Ziran, Liu, Xianping, Zeng, Xiangyong
Format: Article
Language:English
Subjects:
Finite field
Permutation quadrinomial
Permutation trinomial
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Summary:This paper revisits the quadrinomials x3q+a1x2q+1+a2xq+2+a3x3 over Fq2, where q is a power of 2. We propose a more comprehensive characterization of the coefficients that give rise to new permutation quadrinomials. The new characterization not only contains those coefficients given in [20], but also seems to completely cover all the coefficients that yield permutation quadrinomials, which is evidenced by exhaustive searches on small finite fields.
ISSN:1071-5797
1090-2465
DOI:10.1016/j.ffa.2019.04.008