Value sets of Dickson polynomials over Galois rings

AbstractThe Galois ring GR(pn, m) is a finite extension of the ring of integers modulo pn. We consider Dickson polynomials gd(x, a) over Galois rings. In particular, we find an estimate of the cardinality of the value set {gd(x, a)∥ ∈ GR(pn, m)} and determine the cardinality of the preimage of gd(x, a) in certain cases