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

J. Rifà; V. A. Zinoviev

doi:https://doi.org/10.1016/j.disc.2009.03.004

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

J. Rifà, V. A. Zinoviev

Department of Information and Communications Engineering

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

11 Citations (Scopus)

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 ≥ 2, there exist two codes in the constructed class with d = 3, covering radius ρ and lengths (frac(2 ρ, 2)) and (frac(2 ρ + 1, 2)), respectively. The corresponding distance-transitive graphs, which can be defined as coset graphs of these completely transitive codes are described. © 2009 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	5011-5016
Journal	Discrete Mathematics
Volume	309
DOIs	https://doi.org/10.1016/j.disc.2009.03.004
Publication status	Published - 28 Aug 2009

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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title = "On a class of binary linear completely transitive codes with arbitrary covering radius",

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 ≥ 2, there exist two codes in the constructed class with d = 3, covering radius ρ and lengths (frac(2 ρ, 2)) and (frac(2 ρ + 1, 2)), respectively. The corresponding distance-transitive graphs, which can be defined as coset graphs of these completely transitive codes are described. {\textcopyright} 2009 Elsevier B.V. All rights reserved.",

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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year = "2009",

month = aug,

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doi = "https://doi.org/10.1016/j.disc.2009.03.004",

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T1 - On a class of binary linear completely transitive codes with arbitrary covering radius

AU - Rifà, J.

AU - Zinoviev, V. A.

PY - 2009/8/28

Y1 - 2009/8/28

N2 - 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 ≥ 2, there exist two codes in the constructed class with d = 3, covering radius ρ and lengths (frac(2 ρ, 2)) and (frac(2 ρ + 1, 2)), respectively. The corresponding distance-transitive graphs, which can be defined as coset graphs of these completely transitive codes are described. © 2009 Elsevier B.V. All rights reserved.

AB - 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 ≥ 2, there exist two codes in the constructed class with d = 3, covering radius ρ and lengths (frac(2 ρ, 2)) and (frac(2 ρ + 1, 2)), respectively. The corresponding distance-transitive graphs, which can be defined as coset graphs of these completely transitive codes are described. © 2009 Elsevier B.V. All rights reserved.

KW - Completely regular code

KW - Completely transitive code

KW - Covering radius

KW - Distance-regular graph

KW - Distance-transitive graph

KW - Intersection numbers

KW - Outer distance

KW - Uniformly packed code

U2 - https://doi.org/10.1016/j.disc.2009.03.004

DO - https://doi.org/10.1016/j.disc.2009.03.004

M3 - Article

SN - 0012-365X

VL - 309

SP - 5011

EP - 5016

JO - Discrete Mathematics

JF - Discrete Mathematics

ER -

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

Abstract

Keywords

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