Yesterday's post suggests a review of the following —
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Andries Brouwer, preprint, 1982:
"The Witt designs, Golay codes and Mathieu groups" Pages 8-9: Substructures of S(5, 8, 24) An octad is a block of S(5, 8, 24). Theorem 5.1
Let B0 be a fixed octad. The 30 octads disjoint from B0
the design of the points and affine hyperplanes in AG(4, 2), Proof…. … (iv) We have AG(4, 2).
(Proof: invoke your favorite characterization of AG(4, 2) An explicit construction of the vector space is also easy….) |
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