%I #20 Apr 13 2024 04:33:30
%S 1,2,2,2,3,4,3,4,4,4,5,6,5,6,6,6,7,8,7,8,8,8
%N Highest minimal Hamming distance of any Type 4^H+ Hermitian additive self-dual code over GF(4) of length n.
%C The sequence continues: a(23) = 8 or 9, a(24) = 8, 9 or 10, a(25) = 8 or 9, ...
%D P. Gaborit and A. Otmani, Experimental construction of self-dual codes, Preprint.
%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 A. R. Calderbank, E. M. Rains, P. W. Shor and N. J. A. Sloane, <a href="http://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, <a href="http://www.unilim.fr/pages_perso/philippe.gaborit/SD/">Tables of Self-Dual Codes</a>
%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>).
%F Conjectures from _Chai Wah Wu_, Apr 13 2024: (Start)
%F a(n) = a(n-1) + a(n-6) - a(n-7) for n > 7.
%F G.f.: x*(-2*x^6 + x^5 + x^4 + x + 1)/(x^7 - x^6 - x + 1). (End)
%Y Cf. A105674, A105675, A105676, A105677, A105678, A066016, A105681, A105682.
%Y A105687 gives the number of codes with this minimal distance.
%K nonn,more
%O 1,2
%A _N. J. A. Sloane_. Entry revised May 06 2005