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If these 3 points are on a line, we have a codeword and no single change to it will result in a codeword. If these 3 points are not a line, there is a unique point we can add to form a quadrangle, which is the complement of a line in our plane, thus a codeword-removing or adding any other point will not create a codeword.

Bill Cherowitzo
2001-12-11