A016729 Highest minimal Hamming distance of any Type 4^H+ Hermitian additive self-dual code over GF(4) of length n.

1, 2, 2, 2, 3, 4, 3, 4, 4, 4, 5, 6, 5, 6, 6, 6, 7, 8, 7, 8, 8, 8

Offset: 1

Author

N. J. A. Sloane. Entry revised May 06 2005

Keywords

• nonn
• more

Comments

The sequence continues: a(23) = 8 or 9, a(24) = 8, 9 or 10, a(25) = 8 or 9, ...

References

• P. Gaborit and A. Otmani, Experimental construction of self-dual codes, Preprint.

Links

• G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
• 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, Tables of Self-Dual Codes
• 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. A105674, A105675, A105676, A105677, A105678, A066016, A105681, A105682.

A105687 gives the number of codes with this minimal distance.

Formula

Conjectures from Chai Wah Wu, Apr 13 2024: (Start)

a(n) = a(n-1) + a(n-6) - a(n-7) for n > 7.

G.f.: x*(-2*x^6 + x^5 + x^4 + x + 1)/(x^7 - x^6 - x + 1). (End)