Relating Doubly-Even Error-Correcting Codes, Graphs, and Irreducible Representations of N-Extended Supersymmetry

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Doran, C. F.
Faux, M. G.
Gates Jr, S. J.
Hubsch, T.
Iga, K. M.
Landweber, G. D.
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Abstract
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Previous work has shown that the classification of indecomposable off-shell representations of N-supersymmetry, depicted as Adinkras, may be factored into specifying the topologies available to Adinkras, and then the height-assignments for each topological type. The latter problem being solved by a recursive mechanism that generates all height-assignments within a topology, it remains to classify the former. Herein we show that this problem is equivalent to classifying certain (1) graphs and (2) error-correcting codes.
Comment: 19 pages
Keywords
High Energy Physics - Theory, Mathematical Physics, Mathematics - Combinatorics
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