On $q$-ary linear completely regular codes with $\rho=2$ and antipodal dual
Joaquim Borges - Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, 08193-Bellaterra, Spain (email)
Abstract: We characterize all $q$-ary linear completely regular codes with covering radius $\rho=2$ 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 $\rho=2$, 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 $\rho=2$ and antipodal dual, some interesting properties on self-duality and lifted codes are pointed out.
Keywords: Linear completely regular codes, completely transitive codes, covering radius.
Received: February 2010; Available Online: November 2010.
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