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arXiv · 1605.03375

On Some Permutation Binomials and Trinomials Over $\mathbb{F}_{2^n}$

Srimanta Bhattacharya·Sumanta Sarkar
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Abstract

In this work, we completely characterize (i) permutation binomials of the form $x^{{{2^n -1}\over {2^t-1}}+1}+ ax \in \mathbb{F}_{2^n}[x], n = 2^st, a \in \mathbb{F}_{2^{2t}}^{*}$, and (ii) permutation trinomials of the form $x^{2^s+1}+x^{2^{s-1}+1}+αx \in \mathbb{F}_{2^t}[x]$, \end{enumerate} where $s,t$ are positive integers. The first result, which was our primary motivation, is a consequence of the second result. The second result may be of independent interest.

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Srimanta Bhattacharya, Sumanta Sarkar. 2016-05-11. On Some Permutation Binomials and Trinomials Over $\mathbb{F}_{2^n}$. https://arxiv.org/abs/1605.03375

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