On the number of nonequivalent propelinear extended perfect codes

J. Borges; I. Yu Mogilnykh Mogilnykh; J. Rifà; F. Solov'eva

On the number of nonequivalent propelinear extended perfect codes

J. Borges, I. Yu Mogilnykh Mogilnykh, J. Rifà, F. Solov'eva

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Resum

The paper proves that there exists an exponential number of nonequivalent pro- pelinear extended perfect binary codes of length growing to infinity. Specifically, it is proved that all transitive extended perfect binary codes found by Potapov (2007) are propelinear. All such codes have small rank, which is one more than the rank of the extended Hamming code of the same length. We investigate the properties of these codes and show that any of them has a normalized propelinear representation.

Idioma original	Anglès
Revista	Electronic Journal of Combinatorics
Volum	20
Número	2
Estat de la publicació	Publicada - 24 de maig 2013

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title = "On the number of nonequivalent propelinear extended perfect codes",

abstract = "The paper proves that there exists an exponential number of nonequivalent pro- pelinear extended perfect binary codes of length growing to infinity. Specifically, it is proved that all transitive extended perfect binary codes found by Potapov (2007) are propelinear. All such codes have small rank, which is one more than the rank of the extended Hamming code of the same length. We investigate the properties of these codes and show that any of them has a normalized propelinear representation.",

keywords = "Binary codes, Extended perfect codes, Normalized propelinear structures, Propelinear codes",

author = "J. Borges and Mogilnykh, {I. Yu Mogilnykh} and J. Rif{\`a} and F. Solov'eva",

year = "2013",

month = may,

day = "24",

language = "English",

volume = "20",

journal = "Electronic Journal of Combinatorics",

issn = "1077-8926",

publisher = "Electronic Journal of Combinatorics",

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T1 - On the number of nonequivalent propelinear extended perfect codes

AU - Borges, J.

AU - Mogilnykh, I. Yu Mogilnykh

AU - Rifà, J.

AU - Solov'eva, F.

PY - 2013/5/24

Y1 - 2013/5/24

N2 - The paper proves that there exists an exponential number of nonequivalent pro- pelinear extended perfect binary codes of length growing to infinity. Specifically, it is proved that all transitive extended perfect binary codes found by Potapov (2007) are propelinear. All such codes have small rank, which is one more than the rank of the extended Hamming code of the same length. We investigate the properties of these codes and show that any of them has a normalized propelinear representation.

AB - The paper proves that there exists an exponential number of nonequivalent pro- pelinear extended perfect binary codes of length growing to infinity. Specifically, it is proved that all transitive extended perfect binary codes found by Potapov (2007) are propelinear. All such codes have small rank, which is one more than the rank of the extended Hamming code of the same length. We investigate the properties of these codes and show that any of them has a normalized propelinear representation.

KW - Binary codes

KW - Extended perfect codes

KW - Normalized propelinear structures

KW - Propelinear codes

M3 - Article

SN - 1077-8926

VL - 20

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

IS - 2

ER -

On the number of nonequivalent propelinear extended perfect codes

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