A090899 -id:A090899 - cp's OEIS frontend

A094927 Number of nonisomorphic (possibly decomposable) self-dual quantum codes on n qubits.

Original entry on oeis.org

1, 2, 3, 6, 11, 26, 59, 182, 675, 3990, 45144, 1323363

Offset: 1

Lars Eirik Danielsen (larsed(AT)ii.uib.no) and Matthew G. Parker (matthew(AT)ii.uib.no), Jun 17 2004

nonn

Also number of nonisomorphic (indecomposable or decomposable) self-dual codes of Type 4^H+ and length n.

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.

Lars Eirik Danielsen and Matthew G. Parker, Spectral Orbits and Peak-to-Average Power Ratio of Boolean Functions with respect to the {I,H,N}^n Transform, (2005), arxiv:cs/0504102. In Sequences and Their Applications-SETA 2004, Lecture Notes in Computer Science, Volume 3486/2005, Springer-Verlag. [Added by N. J. A. Sloane, Jul 08 2009]
Anatoly Dymarsky and Alfred Shapere, Quantum stabilizer codes, lattices, and CFTs, arXiv:2009.01244 [hep-th], 2020.
G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

See A090899 for more information. Cf. also A110302, A110306.

A110302 Number of inequivalent indecomposable self-dual codes of Type {4^H+}_II and length 2n.

Original entry on oeis.org

1, 1, 1, 4, 14, 103, 2926

Offset: 0

N. J. A. Sloane, Sep 09 2005

nonn

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.

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

Cf. A090899, A094927, A110306.

A110306 Number of inequivalent (indecomposable or decomposable) self-dual codes of Type {4^H+}_II and length 2n.

Original entry on oeis.org

1, 1, 2, 6, 21, 128, 3079

Offset: 0

N. J. A. Sloane, Sep 09 2005

L. E. Danielsen and M. G. Parker, On the classification of all self-dual additive codes over GF(4) of length up to 12, arXiv:math/0504522 [math.CO], 2005-2006.
L. E. Danielsen and M. G. Parker, On the classification of all self-dual additive codes over GF(4) of length up to 12, J. Combin. Theory A 113 (7) (2006) 1351-1367.
W. C. Huffman, On the classification and enumeration of self-dual codes, Finite Fields Applic., 11 (2005), 451-490.
W. C. Huffman, Additive self-dual codes over F_4 with an automorphism of odd prime order, Adv. Math. Commun., 1 (2007), 357-398.
G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

Cf. A090899, A094927, A110302.

A151827 Number of indecomposable self-dual additive codes of length n over GF(4) with minimal distance 4.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 5, 8, 120, 2506, 195455

Offset: 2

N. J. A. Sloane, Jul 12 2009

nonn

Lars Eirik Danielsen and Matthew G. Parker, Spectral Orbits and Peak-to-Average Power Ratio of Boolean Functions with respect to the {I,H,N}^n Transform, (2005), arxiv:cs/0504102. In Sequences and Their Applications-SETA 2004, Lecture Notes in Computer Science, Volume 3486/2005, Springer-Verlag.

Cf. A151825, A151826, A090899.

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.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, May 06 2005

nonn

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.

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).

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.

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

A151825 Number of indecomposable self-dual additive codes of length n over GF(4) with minimal distance 2.

Original entry on oeis.org

1, 1, 2, 3, 9, 22, 85, 363, 2436, 26750, 611036

Offset: 2

N. J. A. Sloane, Jul 12 2009

nonn

Lars Eirik Danielsen and Matthew G. Parker, Spectral Orbits and Peak-to-Average Power Ratio of Boolean Functions with respect to the {I,H,N}^n Transform, (2005), arxiv:cs/0504102. In Sequences and Their Applications-SETA 2004, Lecture Notes in Computer Science, Volume 3486/2005, Springer-Verlag

Cf. A151826, A151827, A090899.

A151826 Number of indecomposable self-dual additive codes of length n over GF(4) with minimal distance 3.

Original entry on oeis.org

0, 0, 0, 1, 1, 4, 11, 69, 576, 11200, 467513

Offset: 2

N. J. A. Sloane, Jul 12 2009

nonn

Lars Eirik Danielsen and Matthew G. Parker, Spectral Orbits and Peak-to-Average Power Ratio of Boolean Functions with respect to the {I,H,N}^n Transform, (2005), arxiv:cs/0504102. In Sequences and Their Applications-SETA 2004, Lecture Notes in Computer Science, Volume 3486/2005, Springer-Verlag.

Cf. A151825, A151827, A090899.

A385629 Number of equivalence classes of connected 4-regular graphs on n unlabeled nodes up to local complementation.

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 2, 6, 13, 56, 261

Offset: 1

Tristan Cam, Aug 09 2025

Number of equivalences classes of 4-regular graphs on n nodes up to a sequence of local complementation or isomorphism.
a(n) is necessarily less than:
  A033301(n) (number of non-isomorphic, not necessarily connected 4-regular graphs);
  A006820(n) (number of non-isomophic connected 4-regular graphs);
  A090899(n) (number of local equivalence classes of connected graphs); and
  A156800(n) (number of equivalence classes for connected graphs up to pivots and isomorphism).
This is relevant in the study of optimal quantum circuit synthesis for graph state preparation.

			There are only two 4-regular graphs with 7 nodes and they are not equivalent up to a sequence of local complementation, thus a(7) = 2.

Niels Bohr Institute Center for Hybrid Quantum Networks, graph_table (github)
Tristan Cam, Cyril Gavoille, Yvan Le Borgne, and Simon Martiel, Universal Graph Theory Operations for Graph State Preparation

Cf. A006820, A033301, A090899, A156800.

A386962 Number of equivalence classes of connected 3-regular graphs on 2n unlabeled nodes up to local complementation.

Original entry on oeis.org

0, 1, 2, 4, 15, 60

Offset: 1

Tristan Cam, Aug 11 2025

Number of equivalences classes of 3-regular graphs on 2n nodes up to a sequence of local complementation or isomorphism, also called orbits for the local equivalence relation.
a(n) is necessarily less than:
  A005638(n) (number of non-isomorphic, not necessarily connected 3-regular graphs);
  A002851(n) (number of non-isomophic connected 3-regular graphs);
  A090899(n) (number of local equivalence classes of connected graphs); and
  A156800(n) (number of equivalence classes for connected graphs up to pivots and isomorphism).
This is relevant in the study of optimal quantum circuit synthesis for graph state preparation.

			There are only two 3-regular graphs with 6 nodes and they are not equivalent up to a sequence of local complementation, thus a(3) = 2.

Niels Bohr Institute Center for Hybrid Quantum Networks, graph_table (github)
Tristan Cam, Cyril Gavoille, Yvan Le Borgne, and Simon Martiel, Universal Graph Theory Operations for Graph State Preparation

Cf. A002851, A005638, A090899, A156800.

cp's OEIS Frontend

A094927 Number of nonisomorphic (possibly decomposable) self-dual quantum codes on n qubits.

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A110302 Number of inequivalent indecomposable self-dual codes of Type {4^H+}_II and length 2n.

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A110306 Number of inequivalent (indecomposable or decomposable) self-dual codes of Type {4^H+}_II and length 2n.

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A151827 Number of indecomposable self-dual additive codes of length n over GF(4) with minimal distance 4.

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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.

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A151825 Number of indecomposable self-dual additive codes of length n over GF(4) with minimal distance 2.

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A151826 Number of indecomposable self-dual additive codes of length n over GF(4) with minimal distance 3.

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A385629 Number of equivalence classes of connected 4-regular graphs on n unlabeled nodes up to local complementation.

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A386962 Number of equivalence classes of connected 3-regular graphs on 2n unlabeled nodes up to local complementation.

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