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Demonstration of a Perfect Code from the Fano Plane

The weight $ w$(x), x $ \epsilon$ V, of a vector is the number of nonzero positions of the vector.

Consider the following subset of the Fano plane: (1) the empty set, (2) the whole plane, (3) the lines of the plane, and (4) the complements of the lines of the planes. These form a perfect 1-error correcting code over GF(2), where $ n=7$.


Bill Cherowitzo 2001-12-11