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Keywords:
finite fields; permutation polynomials
finite fields; permutation polynomials
Summary:
A quasi-permutation polynomial is a polynomial which is a bijection from one subset of a finite field onto another with the same number of elements. This is a natural generalization of the familiar permutation polynomials. Basic properties of quasi-permutation polynomials are derived. General criteria for a quasi-permutation polynomial extending the well-known Hermite's criterion for permutation polynomials as well as a number of other criteria depending on the permuted domain and range are established. Different types of quasi-permutation polynomials and the problem of counting quasi-permutation polynomials of fixed degree are investigated.
References:
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