A new construction for the extended binary golay code

Suat Karadeniz, Bahattin Yildiz

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We give a new construction of the extended binary Golay code. The construction is carried out by taking the Gray image of a self-dual linear code over the ring R = F+2 + uF2 + vF2 + uvF2 of length 6 and size 212.Writing a typical generating matrix of the form [I3|A], with A being a 3×3 matrix over R, and finding some dependencies among the entries of A, we are able to set a general form for the generating matrices of self-dual codes of length 6. Using some special properties of elements of R, we end up with a family of generating matrices all of which give us the extended binary Golay code. We also prove the minimum distance property analytically.

Original languageEnglish (US)
Pages (from-to)69-72
Number of pages4
JournalApplied Mathematics and Information Sciences
Issue number1
StatePublished - Jan 2014
Externally publishedYes


  • Codes over rings
  • Extended binary Golay code
  • Extremal codes
  • Gray map
  • Lee weight
  • Self-dual codes

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics


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