A note on a class of quadratic permutations over \({\mathbb F}_{{2^n}}\). (English) Zbl 1195.11159

Laigle-Chapuy, Yann

Boztaş, Serdar (ed.) et al., Applied algebra, algebraic algorithms and error-correcting codes. 17th international symposium, AAECC-17, Bangalore, India, December 16–20, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-77223-1/pbk). Lecture Notes in Computer Science 4851, 130-137 (2007).

Summary: Finding new classes of permutation polynomials is a challenging problem. Blockhuis at al. investigated the permutation behavior of polynomials of the form \(\sum_{i=0}^{n-1}a_iX^{2^i+1}\) over \({\mathbb F}_{{2^n}}\). In this paper, we extend their results and propose as a new conjecture that if \(n = 2^{e }\) then \(X ^{2}\) is the only unitary permutation polynomial of this type.
For the entire collection see [Zbl 1133.94006].

MSC:

11T06

Polynomials over finite fields