A105687 Number of inequivalent codes attaining highest minimal Hamming distance of any Type 4^H+ Hermitian additive self-dual code over GF(4) of length n.

1, 1, 1, 3, 1, 1, 4, 5, 8, 120, 1, 1

Offset: 1

Author

N. J. A. Sloane, May 06 2005

Keywords

• nonn

References

• 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.
• 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.

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), IEEE Trans. Inform. Theory, 44 (1998), 1369-1387.
• L. E. Danielsen, Database of Self-Dual Quantum Codes.
• L. E. Danielsen and M. G. Parker, On the classification of all self-dual additive codes over GF(4) of length up to 12, preprint, 2005.
• 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. A094927, A090899, A105674, A105675, A105676, A105677, A105678, A016729, A066016, A105681, A105682.

A016729 gives the minimal distance of these codes.

A094927 gives the number of inequivalent codes of any distance.

Extensions

Corrected and extended to 12 terms by Lars Eirik Danielsen (larsed(AT)ii.uib.no) and Matthew G. Parker (matthew(AT)ii.uib.no), Jun 30 2005