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New methods for generating permutation polynomials over finite fields. (English) Zbl 1245.11114
Summary: We present two methods for generating linearized permutation polynomials over an extension of a finite field \(\mathbb F_q\). These polynomials are parameterized by an element of the extension field and are permutation polynomials for all nonzero values of the element. For the case of the extension degree being odd and the size of the ground field satisfying \(q \equiv 3\pmod 4\), these parameterized linearized permutation polynomials can be used to derive non-parameterized nonlinear permutation polynomials via a recent result of C. Ding et al. [Sci. China, Ser. A 52, No. 4, 639–647 (2009; Zbl 1215.11113)] (the citation given in the paper contains errors).

MSC:
11T06 Polynomials over finite fields
12E20 Finite fields (field-theoretic aspects)
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