Abstract
Let r be a prime power and q=rm. For 0≤i≤m−1, let fi∈Fr[X] be q-linearized and ai∈Fq. Assume that z∈F‾r satisfies the equation ∑i=0m−1aifi(z)ri=0, where ∑i=0m−1aifiri∈Fq[X] is an r-linearized polynomial. It is shown that z satisfies a q-linearized polynomial equation with coefficients in Fr. This result provides an explanation for numerous permutation polynomials previously obtained through computer search.
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