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arXiv · 0905.3178

SQS-graphs of Solov'eva-Phelps codes

Italo J. Dejter
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Abstract

A 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.

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Italo J. Dejter. 2009-05-19. SQS-graphs of Solov'eva-Phelps codes. https://arxiv.org/abs/0905.3178

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