Some design theoretic results on the Conway group .0.

Fairbairn, Ben

Displaying similar documents to “Some design theoretic results on the Conway group .0.”

Codes, lattices, and Steiner systems.

Solé, Patrick (1997)

The Electronic Journal of Combinatorics [electronic only]

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Another 80-dimensional extremal lattice

Mark Watkins (2012)

Journal de Théorie des Nombres de Bordeaux

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We show that the unimodular lattice associated to the rank 20 quaternionic matrix group ${SL}_{2} (F_{41}) \otimes {\tilde{S}}_{3} \subset {GL}_{80} (Z)$ is a fourth example of an 80-dimensional extremal lattice. Our method is to use the positivity of the $Θ$ -series in conjunction with an enumeration of all the norm 10 vectors. The use of Aschbacher’s theorem on subgroups of finite classical groups (reliant on the classification of finite simple groups) provides one proof that this lattice is distinct from the previous three, while computing the inner...

Lattice-Like Total Perfect Codes

Carlos Araujo, Italo Dejter (2014)

Discussiones Mathematicae Graph Theory

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A contribution is made to the classification of lattice-like total perfect codes in integer lattices Λn via pairs (G, Φ) formed by abelian groups G and homomorphisms Φ: Zn → G. A conjecture is posed that the cited contribution covers all possible cases. A related conjecture on the unfinished work on open problems on lattice-like perfect dominating sets in Λn with induced components that are parallel paths of length > 1 is posed as well.