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A105687
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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.
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2
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1, 1, 1, 3, 1, 1, 4, 5, 8, 120, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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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.
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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).
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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.
Sequence in context: A104730 A131238 A133380 * A058879 A160870 A025255
Adjacent sequences: A105684 A105685 A105686 * A105688 A105689 A105690
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 06 2005
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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.
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