On a class of binary linear completely transitive codes with arbitrary covering radius

doi:10.1016/j.disc.2009.03.004

Discrete Mathematics

Volume 309, Issue 16, 28 August 2009, Pages 5011-5016

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Abstract

An infinite class of new binary linear completely transitive (and so, completely regular) codes is given. The covering radius of these codes is growing with the length of the code. In particular, for any integer $ρ \geq 2$ , there exist two codes in the constructed class with $d = 3$ , covering radius $ρ$ and lengths $(\binom{2 ρ}{2})$ and $(\binom{2 ρ + 1}{2})$ , respectively. The corresponding distance-transitive graphs, which can be defined as coset graphs of these completely transitive codes are described.

Keywords

Completely regular code

Completely transitive code

Covering radius

Distance-regular graph

Distance-transitive graph

Intersection numbers

Outer distance

Uniformly packed code

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^☆: This work has been partially supported by the Spanish MEC Grants MTM2006-03250, TSI2006-14005-C02-01 and PCI2006-A7-0616 as well as by the Russian fund of fundamental research (the number of the project, 06 - 01 - 00226).

Discrete Mathematics

On a class of binary linear completely transitive codes with arbitrary covering radius☆

Abstract

Keywords