On some permutation binomials and trinomials over F2n

In this work, we completely characterize (1) permutation binomials of the form x 2 n - 1 2 t - 1 + 1 + a x ∈ F 2 n [ x ] , n = 2 s t , a ∈ F 2 2 t ∗ , and (2) permutation trinomials of the form x 2 s + 1 + x 2 s - 1 + 1 + α x ∈ F 2 t [ x ] , where s ,  t are positive integers. The first result, whic...

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Bibliographic Details
Published in:Designs, codes, and cryptography codes, and cryptography, 2017, Vol.82 (1-2), p.149-160
Main Authors: Bhattacharya, Srimanta, Sarkar, Sumanta
Format: Article
Language:English
Subjects:
Circuits
Coding and Information Theory
Computer Science
Cryptology
Data Structures and Information Theory
Discrete Mathematics in Computer Science
Information and Communication
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Summary:In this work, we completely characterize (1) permutation binomials of the form x 2 n - 1 2 t - 1 + 1 + a x ∈ F 2 n [ x ] , n = 2 s t , a ∈ F 2 2 t ∗ , and (2) permutation trinomials of the form x 2 s + 1 + x 2 s - 1 + 1 + α x ∈ F 2 t [ x ] , 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.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-016-0229-0