  Starting from some linear algebraic data (a Weyl-group invariant bilinear
form) and some arithmetic data (a bilinear Steinberg symbol), we construct a
cover of a Kac-Moody group generalizing the work of Matsumoto. Specializing our
construction over non-archimedean local fields, for each positive integer n we
obtain the notion of $n$-fold metaplectic covers of Kac-Moody groups. In this
setting, we prove a Casselman-Shalika type formula for Whittaker functions.
