Geodesic
On the number of nonequivalent propelinear extended perfect codes
Joaquim Borges1 ; Ivan Yu. Mogilnykh2 ; Josep Rifà1 ; Faina I. Solov'eva2
1Universitat Autònoma de Barcelona
2Sobolev Institute of Mathematics and Novosibirsk State University
The electronic journal of combinatorics, Tome 20 (2013) no. 2
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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.
DOI : 10.37236/3220
Classification : 94B25, 94B60
Mots-clés : binary codes, extended perfect codes, normalized propelinear structures, propelinear codes

Joaquim Borges  1   ; Ivan Yu. Mogilnykh  2   ; Josep Rifà  1   ; Faina I. Solov'eva  2

1 Universitat Autònoma de Barcelona
2 Sobolev Institute of Mathematics and Novosibirsk State University 
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     title = {On the number of nonequivalent propelinear extended perfect codes},
     journal = {The electronic journal of combinatorics},
     year = {2013},
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     doi = {10.37236/3220},
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Joaquim Borges; Ivan Yu. Mogilnykh; Josep Rifà; Faina I. Solov'eva. On the number of nonequivalent propelinear extended perfect codes. The electronic journal of combinatorics, Tome 20 (2013) no. 2. doi: 10.37236/3220

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