A New Construction for the Extended Binary Golay Code

Authors

Suat Karadeniz, Department of mathematics, Fatih University, 34500, Istanbul, Turkey
Bahattin Yildiz

Author Country (or Countries)

Turkey

Abstract

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 = F2+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.

Suggested Reviewers

N/A

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/080107

Recommended Citation

Karadeniz, Suat and Yildiz, Bahattin (2014) "A New Construction for the Extended Binary Golay Code," Applied Mathematics & Information Sciences: Vol. 08: Iss. 1, Article 7.
DOI: http://dx.doi.org/10.18576/amis/080107
Available at: https://digitalcommons.aaru.edu.jo/amis/vol08/iss1/7