ℤ4-valued quadratic forms and exponential sums

Zopf₄-valued quadratic forms associated with symmetric bilinear forms are studied. A classification of such forms according to their type and rank is derived. This result is used to compute the distribution of certain exponential sums over Galois rings, which occur frequently in the analysis of correlation properties of quaternary sequence sets. The framework is then illustrated by determining the possible correlation values of family S(t) of length 2^m - 1 proposed by Kumar et al.. For odd m the correlation distribution is derived, which involves the computation of the rank distribution of certain symmetric codes in the rank metric.