  In this paper we study equidistant subspace codes, i.e. subspace codes with
the property that each two distinct codewords have the same distance. We
provide an almost complete classification of such codes under the assumption
that the cardinality of the ground field is large enough. More precisely, we
prove that for most values of the parameters, an equidistant code of maximum
cardinality is either a sunflower or the orthogonal of a sunflower. We also
study equidistant codes with extremal parameters, and establish general
properties of equidistant codes that are not sunflowers. Finally, we propose a
systematic construction of equidistant codes based on our previous construction
of partial spread codes, and provide an efficient decoding algorithm.
