Complete permutation monomials of degree $1+rac{q^n-1}{q-1}$ over the finite field with $q^n$ elements in odd characteristic, for $n+1$ a prime and (n+1)^4 less than q, are classified. As a corollary, a conjecture by Wu, Li, Helleseth, and Zhang is proven in odd characteristic. When n + 1 is a power of the characteristic we provide some new examples. Indecomposable exceptional polynomials of degree 8 and 9 are also classified.

Complete permutation polynomials from exceptional polynomials

BARTOLI, DANIELE;GIULIETTI, Massimo;ZINI, GIOVANNI
2017-01-01

Abstract

Complete permutation monomials of degree $1+rac{q^n-1}{q-1}$ over the finite field with $q^n$ elements in odd characteristic, for $n+1$ a prime and (n+1)^4 less than q, are classified. As a corollary, a conjecture by Wu, Li, Helleseth, and Zhang is proven in odd characteristic. When n + 1 is a power of the characteristic we provide some new examples. Indecomposable exceptional polynomials of degree 8 and 9 are also classified.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1400537
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