New Permutation Trinomials Constructed from Fractional Polynomials

Abstract

Permutation trinomials over finite fields consititute an active research due to their simple algebraic form, additional extraordinary properties and their wide applications in many areas of science and engineering. In the present paper, six new classes of permutation trinomials over finite fields of even characteristic are constructed from six fractional polynomials. Further, three classes of permutation trinomials over finite fields of characteristic three are raised. Distinct from most of the known permutation trinomials which are with fixed exponents, our results are some general classes of permutation trinomials with one parameter in the exponents. Finally, we propose a few conjectures.

References in corpus (4)

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Cited by in corpus (5)

• New Permutation Trinomials From Niho Exponents over Finite Fields with Even Characteristic
• On Two Conjectures about Permutation Trinomials over ${\mathbb{F}}_{3^{2k}}$
• Several Classes of Permutation Trinomials over ${\mathbb{F}}_{5^n}$ From Niho Exponents
• A note on permutation polynomials over finite fields
• A new class of permutation trinomials constructed from Niho exponents