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Cubic self-dual binary codes

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5 Author(s)

We study binary self-dual codes with a fixed point free automorphism of order three. All binary codes of that type can be obtained by a cubic construction that generalizes Turyn's. We regard such "cubic" codes of length 3ℓ as codes of length ℓ over the ring F2×F4. Classical notions of Type II codes, shadow codes, and weight enumerators are adapted to that ring. Two infinite families of cubic codes are introduced. New extremal binary codes in lengths ≤ 66 are constructed by a randomized algorithm. Necessary conditions for the existence of a cubic [72,36,16] Type II code are derived.

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Information Theory, IEEE Transactions on  (Volume:49 ,  Issue: 9 )