Structural properties of binary propelinear codes

Joaquim Borges; Ivan Yu. Mogilnykh; Josep Rifà; Faina I. Solov'eva

doi:10.3934/amc.2012.6.329

Article Contents

2012, Volume 6, Issue 3: 329-346. Doi: 10.3934/amc.2012.6.329

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Structural properties of binary propelinear codes

1.
Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, 08193-Bellaterra
2.
Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk
3.
Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, 08193-Bellaterra, Cerdanyola del Vallès

Received: August 31, 2011

Revised: February 29, 2012

Published: July 2012

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Abstract

The paper deals with some structural properties of propelinear binary codes, in particular propelinear perfect binary codes. We consider the connection of transitive codes with propelinear codes and show that there exists a binary code, the Best code of length 10, size 40 and minimum distance 4, which is transitive but not propelinear. We propose several constructions of propelinear codes and introduce a new large class of propelinear perfect binary codes, called normalized propelinear perfect codes. Finally, based on the different values for the rank and the dimension of the kernel, we give a lower bound on the number of nonequivalent propelinear perfect binary codes.

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Mathematics Subject Classification: Primary: 94B60; Secondary: 94B25.

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References

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