New characterisations of the Nordstrom–Robinson codes

Neil Gillespie, Cheryl E. Praeger

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)
269 Downloads (Pure)

Abstract

In his doctoral thesis, Snover proved that any binary (m, 256, δ) code is equivalent to the Nordstrom-Robinson code or the punctured Nordstrom-Robinson code for (m, δ) = (16, 6) or (15, 5) respectively. We prove that these codes are also characterised as completely regular binary codes with (m, δ) = (16, 6) or (15, 5), and moreover, that they are 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.
Original languageEnglish
Pages (from-to)320-330
Number of pages11
JournalBulletin of the London Mathematical Society
Volume49
Issue number2
Early online date9 Feb 2017
DOIs
Publication statusPublished - 3 Apr 2017

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