Five Constructions of Permutation Polynomials over (q²)

الأصل · EN

Four recursive constructions of permutation polynomials over (q²) with those over (q) are developed and applied to a few famous classes of permutation polynomials. They produce infinitely many new permutation polynomials over (q²ℓ) for any positive integer ℓ with any given permutation polynomial over (q). A generic construction of permutation polynomials over (2²ᵐ) with o-polynomials over (2ᵐ) is also presented, and a number of new classes of permutation polynomials over (2²ᵐ) are obtained.