Construct the incidence structure D corresponding to the graph G,
where the blocks of D correspond to the edges of G.
The point graph G of the incidence structure D. The graph G
has the same point set as D and two vertices u and v of G
are adjacent whenever there is a block of D containing both u
and v.
The block graph of the incidence structure D, i.e., the
point graph of the dual of D.
The incidence graph of the incidence structure D. This
bipartite graph has as vertex set the union of the point
set P and block set B of D. A vertex p ∈P is
adjacent to a vertex b ∈B whenever p ∈b.
Given an incidence structure D with v points and a finite field K,
this function returns the linear code C of length v generated by the
characteristic functions of the blocks of D considered
as vectors of the K-space K(v).
The linear code of the Witt 5-(24, 8, 1) design over GF(2) is the
extended Golay code over GF(2).
> D := WittDesign(24);
> C := LinearCode(D, GF(2));
> C eq GolayCode(GF(2), true);
true
V2.28, 13 July 2023