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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)
Let p be a prime and q a power of p. We study the permutation properties of the polynomial g n,q ∈ F p [x] defined by the functional equation a∈Fq (x + a) n = g n,q (x q − x). The polynomial g n,q is a q-ary version of the reversed Dickson polynomial in characteristic 2. We are interested in the parameters (n, e; q) for which g n,q is a permutation(More)