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A New Construction for the Extended Binary Golay Code |
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PP: 69-72 |
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Author(s) |
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Suat Karadeniz,
Bahattin Yildiz,
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Abstract |
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| 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. |
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