On the Number of Nonequivalent Propelinear Extended Perfect Codes
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Published:2013-05-24
Issue:2
Volume:20
Page:
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ISSN:1077-8926
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Container-title:The Electronic Journal of Combinatorics
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language:
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Short-container-title:Electron. J. Combin.
Author:
Borges Joaquim,Mogilnykh Ivan Yu.,Rifà Josep,Solov'eva Faina I.
Abstract
The paper proves that there exists an exponential number of nonequivalent propelinear 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.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
3 articles.
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2. Transitive nonpropelinear perfect codes;Discrete Mathematics;2015-03
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