A New Construction for the Extended Binary Golay Code

作者：Karadeniz Suat; Yildiz Bahattin^*

来源：Applied Mathematics & Information Sciences, 2014, 8(1): 69-72.

DOI：10.12785/amis/080107

• extremal codes
• extended binary Golay code
• Gray map
• Lee weight
• self-dual codes
• codes over rings

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+uF(2)+vF(2)+uvF(2) of length 6 and size 2(12). Writing a typical generating matrix of the form [I-3 vertical bar A], with A being a 3x3 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.

• 出版日期2014-1