On q-ary linear completely regular codes with ρ = 2 and antipodal dual

Joaquim Borges; Josep Rifá; Victor A. Zinoviev

doi:https://doi.org/10.3934/amc.2010.4.567

On q-ary linear completely regular codes with ρ = 2 and antipodal dual

Joaquim Borges, Josep Rifá, Victor A. Zinoviev

Research output: Contribution to journal › Article › Research › peer-review

13 Citations (Scopus)

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
Pages (from-to)	567-578
Journal	Advances in Mathematics of Communications
Volume	4
DOIs	https://doi.org/10.3934/amc.2010.4.567
Publication status	Published - 1 Dec 2010

Keywords

Completely transitive codes
Covering radius
Linear completely regular codes

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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. {\textcopyright} 2010 AIMS-SDU.",

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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

U2 - https://doi.org/10.3934/amc.2010.4.567

DO - https://doi.org/10.3934/amc.2010.4.567

M3 - Article

VL - 4

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EP - 578

ER -