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On a class of permutation polynomials over \(\mathbb{F}_{2^n}\). (English) Zbl 1180.11038
Golomb, Solomon W. (ed.) et al., Sequences and their applications – SETA 2008. 5th international conference, Lexington, KY, USA, September 14–18, 2008 Proceedings. Berlin: Springer (ISBN 978-3-540-85911-6/pbk). Lecture Notes in Computer Science 5203, 368-376 (2008).
Summary: We study permutation polynomials of the shape \(F(X) = G(X) + \gamma \text{Tr}(H(X))\) over \(\mathbb{F}_{2^n}\). We prove that if the polynomial \(G(X)\) is a permutation polynomial or a linearized polynomial, then the considered problem can be reduced to finding Boolean functions with linear structures. Using this observation we describe six classes of such permutation polynomials.
For the entire collection see [Zbl 1155.94003].

MSC:
11T06 Polynomials over finite fields
94A55 Shift register sequences and sequences over finite alphabets in information and communication theory
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
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