Completely regular codes with different parameters giving the same distance-regular coset graphs

J. Rifà; V. A. Zinoviev

doi:10.1016/j.disc.2017.03.001

Completely regular codes with different parameters giving the same distance-regular coset graphs

J. Rifà, V. A. Zinoviev

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Resum

© 2017 Elsevier B.V. We construct several classes of completely regular codes with different parameters, but identical intersection array. Given a prime power q and any two natural numbers a,b, we construct completely transitive codes over different fields with covering radius ρ=min{a,b} and identical intersection array, specifically, one code over Fqr for each divisor r of a or b. As a corollary, for any prime power q, we show that distance regular bilinear forms graphs can be obtained as coset graphs from several completely regular codes with different parameters.

Idioma original	Anglès
Pàgines (de-a)	1649-1656
Revista	Discrete Mathematics
Volum	340
Número	7
DOIs	https://doi.org/10.1016/j.disc.2017.03.001
Estat de la publicació	Publicada - 1 de jul. 2017

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10.1016/j.disc.2017.03.001

https://ddd.uab.cat/record/171453

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@article{70bdd781149344a298c78511f174ce20,

title = "Completely regular codes with different parameters giving the same distance-regular coset graphs",

abstract = "{\textcopyright} 2017 Elsevier B.V. We construct several classes of completely regular codes with different parameters, but identical intersection array. Given a prime power q and any two natural numbers a,b, we construct completely transitive codes over different fields with covering radius ρ=min\{a,b\} and identical intersection array, specifically, one code over Fqr for each divisor r of a or b. As a corollary, for any prime power q, we show that distance regular bilinear forms graphs can be obtained as coset graphs from several completely regular codes with different parameters.",

keywords = "Bilinear forms graph, Completely regular code, Completely transitive code, Coset graph, Distance-regular graph, Distance-transitive graph, Kronecker product construction, Lifting of a field, Uniformly packed code",

author = "J. Rif{\`a} and Zinoviev, \{V. A.\}",

year = "2017",

month = jul,

day = "1",

doi = "10.1016/j.disc.2017.03.001",

language = "English",

volume = "340",

pages = "1649--1656",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier",

number = "7",

}

TY - JOUR

T1 - Completely regular codes with different parameters giving the same distance-regular coset graphs

AU - Rifà, J.

AU - Zinoviev, V. A.

PY - 2017/7/1

Y1 - 2017/7/1

N2 - © 2017 Elsevier B.V. We construct several classes of completely regular codes with different parameters, but identical intersection array. Given a prime power q and any two natural numbers a,b, we construct completely transitive codes over different fields with covering radius ρ=min{a,b} and identical intersection array, specifically, one code over Fqr for each divisor r of a or b. As a corollary, for any prime power q, we show that distance regular bilinear forms graphs can be obtained as coset graphs from several completely regular codes with different parameters.

AB - © 2017 Elsevier B.V. We construct several classes of completely regular codes with different parameters, but identical intersection array. Given a prime power q and any two natural numbers a,b, we construct completely transitive codes over different fields with covering radius ρ=min{a,b} and identical intersection array, specifically, one code over Fqr for each divisor r of a or b. As a corollary, for any prime power q, we show that distance regular bilinear forms graphs can be obtained as coset graphs from several completely regular codes with different parameters.

KW - Bilinear forms graph

KW - Completely regular code

KW - Completely transitive code

KW - Coset graph

KW - Distance-regular graph

KW - Distance-transitive graph

KW - Kronecker product construction

KW - Lifting of a field

KW - Uniformly packed code

UR - https://www.scopus.com/pages/publications/85016398321

U2 - 10.1016/j.disc.2017.03.001

DO - 10.1016/j.disc.2017.03.001

M3 - Article

SN - 0012-365X

VL - 340

SP - 1649

EP - 1656

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 7

ER -

Completely regular codes with different parameters giving the same distance-regular coset graphs

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