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Incidence Structures, Graphs and Codes
Incidence Structures, Graphs and Codes
IncidenceStructure(G) : Grph -> Inc
Construct the incidence structure D corresponding to the graph G,
where the blocks of D correspond to the edges of G.
PointGraph(D) : Inc -> Grph
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.
BlockGraph(D) : Inc -> Grph
The block graph of the incidence structure D, i.e. the
point graph of the dual of D.
IncidenceGraph(D) : Inc -> Grph
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 in P is
adjacent to a vertex b in B whenever p in b.
LinearCode(D, K) : Inc, FldFin -> Code
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)).
Example Design_graphs (H56E12)
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
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