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

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

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.

Original language	English
Journal	Electronic Journal of Combinatorics
Volume	20
Issue number	2
Publication status	Published - 24 May 2013

Keywords

Binary codes
Extended perfect codes
Normalized propelinear structures
Propelinear codes

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Cite this

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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",

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year = "2013",

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journal = "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

VL - 20

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

SN - 1077-8926

IS - 2

ER -