A106169 Number of inequivalent codes attaining highest minimal Hamming distance of any Type (4_II)^H+ even Hermitian additive self-dual code over GF(4) of length 2n.

1, 2, 1, 3, 19, 1, 1020

Offset

1,2

Comments

The minimal distance of these codes is (so far) 2,2,4,4,4,6.

Links

Table of n, a(n) for n=1..7.

C. Bachoc and P. Gaborit, On extremal additive F_4 codes of length 10 to 18, in International Workshop on Coding and Cryptography (Paris, 2001), Electron. Notes Discrete Math. 6 (2001), 10 pp.

A. R. Calderbank, E. M. Rains, P. W. Shor and N. J. A. Sloane, Quantum error correction via codes over GF(4), arXiv:quant-ph/9608006, 1996-1997; IEEE Trans. Inform. Theory, 44 (1998), 1369-1387.

P. Gaborit, W. C. Huffman, J.-L. Kim and V. S. Pless, On additive GF(4) codes, in Codes and Association Schemes (Piscataway, NJ, 1999), A. Barg and S. Litsyn, eds., Amer. Math. Soc., Providence, RI, 2001, pp. 135-149.

G. Hoehn, Self-dual codes over the Kleinian four-group, Math. Ann. 327 (2003), 227-255.

W. C. Huffman, On the classification and enumeration of self-dual codes, Finite Fields Applic., 11 (2005), 451-490.

W. C. Huffman, Additive self-dual codes over F_4 with an automorphism of odd prime order, Adv. Math. Commun., 1 (2007), 357-398.

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998 (Abstract, pdf, ps).

Crossrefs

Cf. A105687.

Cf. also A105674, A105675, A105676, A105677, A105678, A016729, A066016, A105681, A105682.

Sequence in context: A197190 A247482 A156364 * A319493 A340202 A108353

Adjacent sequences: A106166 A106167 A106168 * A106170 A106171 A106172

Keyword

nonn,hard,more

Author

N. J. A. Sloane, May 09 2005

Status

approved