Certain exponential sums over Galois rings and related constructions of families of sequences

Upper bounds for certain exponential sums over Galois rings are presented. The bound may be regarded as the Galois ring analogue of the so called Kloosterman sums and related exponential sums with a Laurent polynomial argument. An application of the bounds to the design of large families of polyphase sequences with good correlation properties is also given. The character sums appear naturally as correlation values of certain families of sequences. To arrive at the families all one has to do is to select representatives of cyclically distinct classes of associated codewords