Abstract
We outline the basics for a systematic study of permutation polynomials on finite fields with characteristic 2, which admit a certain uniform representation. We describe a general technique to confirm the permutation property of such polynomials by algebraic calculations with multivariate polynomials over the two-element field. These computations are simple, but so extensive that they have to be done with computer support. We demonstrate that our method can be applied to all of the presently known classes of uniformly representable permutation polynomials, in particular to the o-polynomials of Glynn and Cherowitzo.
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