  In this note we apply a spectral method to the graph of alternating bilinear
forms. In this way, we obtain upper bounds on the size of an alternating
rank-metric code for given values of the minimum rank distance. We
computationally compare our results with Delsarte's linear programming bound,
observing that they give the same value. For small values of the minimum rank
distance, we are able to establish the equivalence of the two methods. The
problem remains open for larger values.
