New characterisations of the Nordstrom–Robinson codes

Autor: Cheryl E. Praeger, Neil I. Gillespie
Rok vydání: 2017
Předmět:
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