Abstract
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.
Original language | English |
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Pages (from-to) | 567-578 |
Journal | Advances in Mathematics of Communications |
Volume | 4 |
DOIs | |
Publication status | Published - 1 Dec 2010 |
Keywords
- Completely transitive codes
- Covering radius
- Linear completely regular codes