Kumar, PV; Helleseth, T; Calderbank, AR, *Upper bound for Weil exponential sums over Galois rings and applications*,
IEEE Transactions on Information Theory, vol. 41 no. 2
(1995),
pp. 456-468 [doi] .
**Abstract:**

*We present an analog of the well-known Weil-Carlitz-Uchiyama 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 pe, p prime, e ≥ 2. Some new constructions of eight-phase sequences are provided.*