Combinatorics associated with inflections and bitangents of plane quartics
M. Kh. Gizatullin · Izvestiya Mathematics · 2013
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.