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Corresponding Geometry

I hoped to present a projective geometry built upon GF(3) and a Hamming code embedded within as done for the Fano plane. I have been unable to reach this goal. But my research has shown the following results.

Construction techniques of Hamming codes in linear algebra allow corresponding geometric-space constructions.

Specifically, if we take each column of a parity check matrix H and let them correspond to a set S of $ n$ points in a projective space PG($ k-1,q$), then words of the dual code will correspond to complements of hyperplane sections in S.

I do not understand the above stated information.


Bill Cherowitzo 2001-12-11