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Reversed Dickson polynomials over finite fields are obtained from Dickson polynomials D n (x, a) over finite fields by reversing the roles of the indeterminate x and the parameter a. We study reversed Dickson polynomials with emphasis on their permutational properties over finite fields. We show that reversed Dickson permutation polynomials (RDPPs) are(More)
Let p be an odd prime and let f (x) = P k i=1 a i x p α i +1 ∈ F p n [x], where 0 ≤ α 1 < · · · < α k. We consider the exponential sum S(f, n) = P x∈F p n en(f (x)), where en(y) = e 2πiTrn(y)/p , y ∈ F p n , Trn = Tr F p n /Fp. There is an effective way to compute the nullity of the quadratic form Trmn(f (x)) for all integer m > 0. Assuming that all such(More)
Let e be a positive integer, p be an odd prime, q = p e , and Fq be the finite field of q elements. Let f, g ∈ Fq[X, Y ]. The graph G = Gq(f, g) is a bipartite graph with vertex partitions P = F 3 q and L = F 3 q , and edges defined as follows: a vertex (p) = (p 1 , p 2 , p 3) ∈ P is adjacent to a vertex [l] = [l 1 , l 2 , l 3 ] ∈ L if and only if p 2 + l 2(More)