  We study the combined effects of disorder and range of the couplings on the
phase diagram of one-dimensional topological superconductors. We consider an
extended version of the Kitaev chain where hopping and pairing terms couple
many sites. Deriving the conditions for the existence of Majorana zero modes,
we show that either the range and the on-site disorder can greatly enhance the
topological phases characterized by the appearance of one or many Majorana
modes localized at the edges. We consider both a discrete and a continuous
disorder distribution. Moreover we discuss the role of correlated disorder
which might further widen the topological regions. Finally we show that in the
purely long-range regime and in the presence of disorder, the spatial decay of
the edge modes remains either algebraic or exponential, with eventually a
modified localization length, as in the absence of disorder.
