In determining location in a previously mapped region by map-matching, there arises the question of minimum submap size relative to the size of the complete map of the region for unambiguous determination of position. A lower bound for the size of the submap is obtained for quantized binary maps. It is shown that there exist maps (called perfect) such that this lower bound is realized. Of special interest is the construction of a doubly periodic4 \times 4perfect map for a2 \times 2submap. The two-dimensional analogy of perfect maps to shift register codes suggests a possible development of planar error-correcting codes and an application to the two-dimensional range-velocity ambiguity problem of radar.