Structural properties of binary propelinear codes

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

Research output: Contribution to journalArticleResearchpeer-review

14 Citations (Scopus)

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. © 2012 AIMS.
Original languageEnglish
Pages (from-to)329-346
JournalAdvances in Mathematics of Communications
Volume6
Issue number3
DOIs
Publication statusPublished - 1 Aug 2012

Keywords

  • Binary perfect codes
  • Propelinear codes
  • Transitive codes

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