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Permutation and complete permutation polynomials. (English) Zbl 1368.11126
Summary: Polynomials of type \(x^{q + 2} + b x\) over the field \(\mathbb{F}_{q^2}\) and of type \(x^{q^2 + q + 2} + b x\) over \(\mathbb{F}_{q^3}\), where \(q = p^m > 2\) is a power of a prime \(p\) are considered. All cases when these polynomials are permutation polynomials are classified. Therefore, all cases when the polynomials \(b^{- 1} x^{q + 2}\) over \(\mathbb{F}_{q^2}\) and \(b^{- 1} x^{q^2 + q + 2}\) over \(\mathbb{F}_{q^3}\) are the complete permutation polynomials are enumerated.

MSC:
11T06 Polynomials over finite fields
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
12Y05 Computational aspects of field theory and polynomials (MSC2010)
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