An upper bound for Weil exponential sums over Galois rings and applications

We present an analog of the well-known Weil-Carlitz-Uchiyama (1948, 1957) upper bound for exponential sums over finite fields for exponential sums over Galois rings. Some examples are given where the bound is tight. The bound has immediate application to the design of large families of phase-shift-keying sequences having low correlation and an alphabet of size p/sup e/. p, prime, e/spl ges/2. Some new constructions of eight-phase sequences are provided.>