A New Construction for the Extended Binary Golay Code

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 2 12 . Writing a typical generating matrix of the form (I3jA), 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.