New characterisations of the Nordstrom–Robinson codes
Autor: | Cheryl E. Praeger, Neil I. Gillespie |
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Rok vydání: | 2017 |
Předmět: |
Discrete mathematics
Code (set theory) Transitive relation General Mathematics Binary number 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology 16. Peace & justice 01 natural sciences Combinatorics General Relativity and Quantum Cosmology 010201 computation theory & mathematics Converse 0202 electrical engineering electronic engineering information engineering Binary code Mathematics |
Zdroj: | Gillespie, N & Praeger, C E 2017, ' New characterisations of the Nordstrom–Robinson codes ', Bulletin of the London Mathematical Society, vol. 49, no. 2, pp. 320-330 . https://doi.org/10.1112/blms.12016 |
ISSN: | 1469-2120 0024-6093 |
Popis: | In his doctoral thesis, Snover proved that any binary $(m,256,\delta)$ code is equivalent to the Nordstrom-Robinson code or the punctured Nordstrom-Robinson code for $(m,\delta)=(16,6)$ or $(15,5)$ respectively. We prove that these codes are also characterised as \emph{completely regular} binary codes with $(m,\delta)=(16,6)$ or $(15,5)$, and moreover, that they are \emph{completely transitive}. Also, it is known that completely transitive codes are necessarily completely regular, but whether the converse holds has up to now been an open question. We answer this by proving that certain completely regular codes are not completely transitive, namely, the (Punctured) Preparata codes other than the (Punctured) Nordstrom-Robinson code. |
Databáze: | OpenAIRE |
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