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Advances in Mathematics of Communications (AMC)
 

Structural properties of binary propelinear codes

Pages: 329 - 346, Volume 6, Issue 3, August 2012      doi:10.3934/amc.2012.6.329

 
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Joaquim Borges - Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, 08193-Bellaterra, Spain (email)
Ivan Yu. Mogilnykh - Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russian Federation (email)
Josep Rifà - Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, 08193-Bellaterra, Cerdanyola del Vallès, Spain (email)
Faina I. Solov'eva - Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russian Federation (email)

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.

Keywords:  Propelinear codes, transitive codes, binary perfect codes.
Mathematics Subject Classification:  Primary: 94B60; Secondary: 94B25.

Received: September 2011;      Revised: March 2012;      Available Online: August 2012.

 References