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.
Digital Object Identifier (DOI)
Karadeniz, Suat and Yildiz, Bahattin
"A New Construction for the Extended Binary Golay Code,"
Applied Mathematics & Information Sciences: Vol. 08
, Article 7.
Available at: https://dc.naturalspublishing.com/amis/vol08/iss1/7