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

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, find construct good codes for lengths 16 < n < 27. We also classify the extremal additive 4-circulant self-dual codes of lengths 4, 6, 8, 1 2, 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, 6, 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.