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

J. Rifà; V. A. Zinoviev

doi:https://doi.org/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

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

3 Citations (Scopus)

Abstract

© 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.

Original language	English
Pages (from-to)	1649-1656
Journal	Discrete Mathematics
Volume	340
Issue number	7
DOIs	https://doi.org/10.1016/j.disc.2017.03.001
Publication status	Published - 1 Jul 2017

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

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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",

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

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DO - https://doi.org/10.1016/j.disc.2017.03.001

M3 - Article

VL - 340

SP - 1649

EP - 1656

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 7

ER -

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

Abstract

Keywords

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