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%I #16 Aug 06 2024 09:41:20
%S 1,2,1,3,19,1,1020
%N 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.
%C The minimal distance of these codes is (so far) 2,2,4,4,4,6.
%H C. Bachoc and P. Gaborit, <a href="https://doi.org/10.1016/S1571-0653(04)00157-X">On extremal additive F_4 codes of length 10 to 18</a>, in International Workshop on Coding and Cryptography (Paris, 2001), Electron. Notes Discrete Math. 6 (2001), 10 pp.
%H A. R. Calderbank, E. M. Rains, P. W. Shor and N. J. A. Sloane, <a href="https://arxiv.org/abs/quant-ph/9608006">Quantum error correction via codes over GF(4)</a>, arXiv:quant-ph/9608006, 1996-1997; IEEE Trans. Inform. Theory, 44 (1998), 1369-1387.
%H P. Gaborit, W. C. Huffman, J.-L. Kim and V. S. Pless, <a href="https://citeseerx.ist.psu.edu/pdf/750e493600ee8c84682f85998f32e2b1304cfdd9">On additive GF(4) codes</a>, in Codes and Association Schemes (Piscataway, NJ, 1999), A. Barg and S. Litsyn, eds., Amer. Math. Soc., Providence, RI, 2001, pp. 135-149.
%H G. Hoehn, <a href="https://doi.org/10.1007/s00208-003-0440-y">Self-dual codes over the Kleinian four-group</a>, Math. Ann. 327 (2003), 227-255.
%H W. C. Huffman, <a href="https://doi.org/10.1016/j.ffa.2005.05.012">On the classification and enumeration of self-dual codes</a>, Finite Fields Applic., 11 (2005), 451-490.
%H W. C. Huffman, <a href="http://dx.doi.org/10.3934/amc.2007.1.357">Additive self-dual codes over F_4 with an automorphism of odd prime order</a>, Adv. Math. Commun., 1 (2007), 357-398.
%H G. Nebe, E. M. Rains and N. J. A. Sloane, <a href="http://neilsloane.com/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, Springer, Berlin, 2006.
%H E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998 (<a href="http://neilsloane.com/doc/self.txt">Abstract</a>, <a href="http://neilsloane.com/doc/self.pdf">pdf</a>, <a href="http://neilsloane.com/doc/self.ps">ps</a>).
%Y Cf. A105687.
%Y Cf. also A105674, A105675, A105676, A105677, A105678, A016729, A066016, A105681, A105682.
%K nonn,hard,more
%O 1,2
%A _N. J. A. Sloane_, May 09 2005