Abstract:
After a preliminary survey and a description of some small Steiner systems
from the standpoint of the theory of invariants of binary forms, we
construct a binary Golay code (of length 24) using ideas from J. Grassmann's
thesis of 1875. One of our tools is a pair of disjoint Fano planes.
Another application of such pairs and properties of plane quartics
is a construction of a new block design on 28 objects. This block design is
a part of a dissection of the set of 288 Aronhold sevens. The dissection
distributes the Aronhold sevens into 8 disjoint block designs of this type.
Keywords:binary form, invariant, point of inflection, bitangent, plane quartic,
Aronhold seven, block design, Fano plane, Steiner system, Golay code.
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