TY - JOUR
T1 - New characterisations of the Nordstrom-Robinson codes
AU - Gillespie, Neil I.
AU - Praeger, Cheryl E.
PY - 2017/4/1
Y1 - 2017/4/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85012921528&partnerID=8YFLogxK
U2 - 10.1112/blms.12016
DO - 10.1112/blms.12016
M3 - Article
AN - SCOPUS:85012921528
VL - 49
SP - 320
EP - 330
JO - Bulletin of the London Mathematical Society
JF - Bulletin of the London Mathematical Society
SN - 0024-6093
IS - 2
ER -