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Proof

Enumerate the points of the Fano plane. Consider a vector space V over GF(2) where $ n$=7. Let the codewords be constructed as follows. The $ k$th position of the codeword is a 1 if the $ k$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