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Circulant based extremal additive self-dual codes over GF(4)

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2 Author(s)
Gulliver, T.A. ; Dept. of Electr. & Comput. Eng., Univ. of Victoria, BC, Canada ; Jon-Lark Kim

It is well known that the problem of finding stabilizer quantum-error-correcting codes (QECC) is transformed into the problem of finding additive self-orthogonal codes over the Galois field GF(4) under a trace inner product. Our purpose is to classify the extremal additive circulant self-dual codes of lengths up to 15, and construct good codes for lengths 16≤n≤27. We also classify the extremal additive 4-circulant self-dual codes of lengths 4,6,8,12,14, and 16 and most codes of length 10, and construct good codes of even lengths up to 22. Furthermore, we classify the extremal additive bordered 4-circulant self-dual codes of lengths 3,5,7,9,11,13,15, and 17, and construct good codes for lengths 19,21,23, and 25. We give the current status of known extremal (or optimal) additive self-dual codes of lengths 12 to 27.

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Information Theory, IEEE Transactions on  (Volume:50 ,  Issue: 2 )