On the Number of Nonequivalent Propelinear Extended Perfect Codes

  • Joaquim Borges
  • Ivan Yu. Mogilnykh
  • Josep Rifà
  • Faina I. Solov'eva
Keywords: binary codes, extended perfect codes, normalized propelinear structures, propelinear codes


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.

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