Uniqueness of certain completely regular Hadamard codes

Neil I. Gillespie; Cheryl E. Praeger

doi:10.1016/j.jcta.2013.04.006

Uniqueness of certain completely regular Hadamard codes

Neil I. Gillespie^*, Cheryl E. Praeger

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

We classify binary completely regular codes of length m with minimum distance delta for (m, delta) = (12,6) and (11,5). We prove that such codes are unique up to equivalence, and in particular, are equivalent to certain Hadamard codes. Moreover, we prove that these codes are completely transitive.

Original language	English
Pages (from-to)	1394-1400
Number of pages	7
Journal	Journal of Combinatorial Theory, Series A
Volume	120
Issue number	7
Early online date	22 Apr 2013
DOIs	https://doi.org/10.1016/j.jcta.2013.04.006
Publication status	Published - Sept 2013

Keywords

Completely regular codes
Completely transitive codes
Hadamard codes
Mathieu groups
transitive codes
binary

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title = "Uniqueness of certain completely regular Hadamard codes",

abstract = "We classify binary completely regular codes of length m with minimum distance delta for (m, delta) = (12,6) and (11,5). We prove that such codes are unique up to equivalence, and in particular, are equivalent to certain Hadamard codes. Moreover, we prove that these codes are completely transitive.",

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TY - JOUR

T1 - Uniqueness of certain completely regular Hadamard codes

AU - Gillespie, Neil I.

AU - Praeger, Cheryl E.

PY - 2013/9

Y1 - 2013/9

N2 - We classify binary completely regular codes of length m with minimum distance delta for (m, delta) = (12,6) and (11,5). We prove that such codes are unique up to equivalence, and in particular, are equivalent to certain Hadamard codes. Moreover, we prove that these codes are completely transitive.

AB - We classify binary completely regular codes of length m with minimum distance delta for (m, delta) = (12,6) and (11,5). We prove that such codes are unique up to equivalence, and in particular, are equivalent to certain Hadamard codes. Moreover, we prove that these codes are completely transitive.

KW - Completely regular codes

KW - Completely transitive codes

KW - Hadamard codes

KW - Mathieu groups

KW - transitive codes

KW - binary

U2 - 10.1016/j.jcta.2013.04.006

DO - 10.1016/j.jcta.2013.04.006

M3 - Article (Academic Journal)

SN - 0097-3165

VL - 120

SP - 1394

EP - 1400

JO - Journal of Combinatorial Theory, Series A

JF - Journal of Combinatorial Theory, Series A

IS - 7

ER -

Uniqueness of certain completely regular Hadamard codes

Abstract

Keywords

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