2009/05/19 by Italo J. Dejter, Dejter, Italo J.
Computer Science · Engineering · Mathematics · #05C90 #94B25 #Cellular Automata and Applications #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.CO #math.IT #msc:05C90 #msc:94B25
paper · pdf · doi:10.48550/arxiv.0905.3178
14 pages, 15 tables
arxiv created 2009/05/19 · openalex publication_date 2009/05/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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≥κ≥ 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.