On the Classification of Completely Regular Codes with Covering Radius Two and Antipodal Duals

J. Borges; V. A. Zinoviev; D. V. Zinoviev

doi:10.1134/S003294602303002X

On the Classification of Completely Regular Codes with Covering Radius Two and Antipodal Duals

J. Borges^*, V. A. Zinoviev, D. V. Zinoviev

^*Corresponding author for this work

Department of Information and Communications Engineering

Russian Academy of Sciences (RAS)

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

1 Citation (Scopus)

Abstract

We classify all linear completely regular codes which have covering radius and whose dual are antipodal. For this, we firstly show several properties of such dual codes, which are two-weight codes with weights and.

Original language	English
Pages (from-to)	204-216
Number of pages	13
Journal	Problems of Information Transmission
Volume	59
Issue number	3
DOIs	https://doi.org/10.1134/S003294602303002X
Publication status	Published - Jul 2023

Keywords

code with an antipodal dual
code with covering radius 2
difference matrix
equidistant code
Hadamard matrix
Hamming code
Latin square
linear completely regular code
maximal arc
projective oval
two-weight code

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10.1134/S003294602303002X

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title = "On the Classification of Completely Regular Codes with Covering Radius Two and Antipodal Duals",

abstract = "We classify all linear completely regular codes which have covering radius and whose dual are antipodal. For this, we firstly show several properties of such dual codes, which are two-weight codes with weights and.",

keywords = "code with an antipodal dual, code with covering radius 2, difference matrix, equidistant code, Hadamard matrix, Hamming code, Latin square, linear completely regular code, maximal arc, projective oval, two-weight code",

author = "J. Borges and Zinoviev, {V. A.} and Zinoviev, {D. V.}",

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AU - Zinoviev, D. V.

N1 - Publisher Copyright: © Pleiades Publishing, Inc. 2023.

PY - 2023/7

Y1 - 2023/7

N2 - We classify all linear completely regular codes which have covering radius and whose dual are antipodal. For this, we firstly show several properties of such dual codes, which are two-weight codes with weights and.

AB - We classify all linear completely regular codes which have covering radius and whose dual are antipodal. For this, we firstly show several properties of such dual codes, which are two-weight codes with weights and.

KW - code with an antipodal dual

KW - code with covering radius 2

KW - difference matrix

KW - equidistant code

KW - Hadamard matrix

KW - Hamming code

KW - Latin square

KW - linear completely regular code

KW - maximal arc

KW - projective oval

KW - two-weight code

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DO - 10.1134/S003294602303002X

M3 - Article

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SP - 204

EP - 216

JO - Problems of Information Transmission

JF - Problems of Information Transmission

IS - 3

ER -

On the Classification of Completely Regular Codes with Covering Radius Two and Antipodal Duals

Abstract

Keywords

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