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2-design abelian adjacent affine space block design block space called Cayley graph characterization chromatic polynomial codewords coefficient Combinatorial Theory conjecture construction defined deleting deletion-contraction denote digon disjoint dual edges of G embedded example exists extendable extremal code finite flat generalised projective genus geometric graph graph G Graph Theory hypermatroid hyperplane imbed incidence structure incidence structure jt induction intersection isomorphic lattice packing Let G line graph linear code linear space lower subspace Math matroid matroid structure minimum Mobius plane near-triangulation non-zero nonorientable number of points obtained Open Problem orientable parallelism parameters plane of order prime power projective geometry projective plane projective space properties Proposition proved rank Ray-Chaudhuri result satisfies self-dual codes self-dual lattice set of points simple graph Sloane spanned sphere sphere-packing Sprague strongly regular graph subset symmetric design T-critical graph theta-function triangulation underlying matroid vectors vertex set vertices voltage graph imbedding weight enumerator zero