TY - JOUR
T1 - On q-ary linear completely regular codes with ρ = 2 and antipodal dual
AU - Borges, Joaquim
AU - Rifá, Josep
AU - Zinoviev, Victor A.
PY - 2010/12/1
Y1 - 2010/12/1
N2 - We characterize all q-ary linear completely regular codes with covering radius ρ = 2 when the dual codes are antipodal. These completely regular codes are extensions of linear completely regular codes with covering radius 1, which we also classify. For ρ = 2, we give a list of all such codes known to us. This also gives the characterization of two weight linear antipodal codes. Finally, for a class of completely regular codes with covering radius ρ = 2 and antipodal dual, some interesting properties on self-duality and lifted codes are pointed out. © 2010 AIMS-SDU.
AB - We characterize all q-ary linear completely regular codes with covering radius ρ = 2 when the dual codes are antipodal. These completely regular codes are extensions of linear completely regular codes with covering radius 1, which we also classify. For ρ = 2, we give a list of all such codes known to us. This also gives the characterization of two weight linear antipodal codes. Finally, for a class of completely regular codes with covering radius ρ = 2 and antipodal dual, some interesting properties on self-duality and lifted codes are pointed out. © 2010 AIMS-SDU.
KW - Completely transitive codes
KW - Covering radius
KW - Linear completely regular codes
UR - https://www.scopus.com/pages/publications/78649399648
U2 - 10.3934/amc.2010.4.567
DO - 10.3934/amc.2010.4.567
M3 - Article
SN - 1930-5346
VL - 4
SP - 567
EP - 578
JO - Advances in Mathematics of Communications
JF - Advances in Mathematics of Communications
ER -