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Enumerate the points of the Fano plane. Consider a vector space **V** over GF(2) where =7. Let the codewords be constructed as follows. The th position of the codeword is a 1 if the th point belongs to the codeword (geometrically). Else it is a 0.
We need to show that for any given **v**, there is only one distinct codeword to which we can map (decode) it. Let us consider the weight of an arbitrary **v**.

Bill Cherowitzo
2001-12-11