SQS-graphs of Solov'eva-Phelps codes

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dc.creatorDejter, Italo J.
dc.date2009-05-19
dc.date.accessioned2026-07-07T13:16:43Z
dc.date.available2026-07-07T13:16:43Z
dc.descriptionA binary extended 1-perfect code $\mathcal C$ folds over its kernel via the Steiner quadruple systems associated with its codewords. The resulting folding, proposed as a graph invariant for $\mathcal C$, distinguishes among the 361 nonlinear codes $\mathcal C$ of kernel dimension $κ$ obtained via Solov'eva-Phelps doubling construction, where $9\geqκ\geq 5$. Each of the 361 resulting graphs has most of its nonloop edges expressible in terms of lexicographically ordered quarters of products of classes from extended 1-perfect partitions of length 8 (as classified by Phelps) and loops mostly expressible in terms of the lines of the Fano plane.
dc.description14 pages, 15 tables
dc.identifierhttps://arxiv.org/abs/0905.3178
dc.identifierhttp://arxiv.org/abs/0905.3178
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/230881
dc.subjectCombinatorics
dc.subjectInformation Theory
dc.subject05C90; 94B25
dc.titleSQS-graphs of Solov'eva-Phelps codes
dc.typetext

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