Semisymmetric elementary abelian covers of the Möbius-Kantor graph

Let @?"N:X@?->X be a regular covering projection of connected graphs with the group of covering transformations isomorphic to N. If N is an elementary abelian p-group, then the projection @?"N is called p-elementary abelian. The projection @?"N is vertex-transitive (edge-transitive) if some vertex-transitive (edge-transitive) subgroup of Aut X lifts along @?"N, and semisymmetric if it is edge- but not vertex-transitive. The projection @?"N is minimal semisymmetric if @?"N cannot be written as a composition @?"N=@?@?@?"M of two (nontrivial) regular covering projections, where @?"M is semisymmetric. Finding elementary abelian covering projections can be grasped combinatorially via a linear representation of automorphisms acting on the first homology group of the graph. The method essentially reduces to finding invariant subspaces of matrix groups over prime fields (see [A. Malnic, D. Marusic, P. Potocnik, Elementary abelian covers of graphs, J. Algebraic Combin. 20 (2004) 71-97]). In this paper, all pairwise nonisomorphic minimal semisymmetric elementary abelian regular covering projections of the Mobius-Kantor graph, the Generalized Petersen graph GP(8,3), are constructed. No such covers exist for p=2. Otherwise, the number of such covering projections is equal to (p-1)/4 and 1+(p-1)/4 in cases p=5,9,13,17,21(mod24) and p=1(mod24), respectively, and to (p+1)/4 and 1+(p+1)/4 in cases p=3,7,11,15,23(mod24) and p=19(mod24), respectively. For each such covering projection the voltage rules generating the corresponding covers are displayed explicitly.