  The paper proposes to decode Reed-Muller (RM) codes by projecting onto only a
few subspaces such that the number of projections is significantly reduced. It
reveals that the probability that error pairs are canceled simultaneously in
two different projections is determined by their intersection size. Then,
correlation coefficient which indicates the intersection size of two subspaces
in a collection is introduced for collecting subspaces. Simulation results show
that our proposed approach with a small number of projections onto collected
subspaces performs close to the original approach.
