A106167 -id:A106167 - cp's OEIS frontend

A106162 Number of indecomposable Type II binary self-dual codes of length 8n.

Original entry on oeis.org

1, 1, 1, 7, 75, 94251

Offset: 0

N. J. A. Sloane, May 09 2005

J. H. Conway and V. S. Pless, On the enumeration of self-dual codes, J. Comb. Theory, A28 (1980), 26-53.
V. S. Pless, The children of the (32,16) doubly even codes, IEEE Trans. Inform. Theory, 24 (1978), 738-746.

Koichi Betsumiya, Masaaki Harada and Akihiro Munemasa, A Complete Classification of Doubly Even Self-Dual Codes of Length 40, arXiv:1104.3727v3 [math.CO], v3, Aug 02, 2012.
J. H. Conway, V. Pless and N. J. A. Sloane, The Binary Self-Dual Codes of Length Up to 32: A Revised Enumeration, J. Comb. Theory, A28 (1980), 26-53 (Abstract, pdf, ps, Table A, Table D).
G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
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. A003178, A003179, A106163-A106167.

a(4) corrected by John van Rees, Jul 21 2005. It was given as 76 by Conway and Pless and as 74 by Rains and Sloane.

a(5) = 94251 = 94343 - 75 - 7 - 7 - 1 - 1 - 1 (cf. A106163) from Koichi Betsumaya, Aug 11 2012

A106163 Total number of (indecomposable or decomposable) Type II binary self-dual codes of length 8n.

Original entry on oeis.org

1, 1, 2, 9, 85, 94343

Offset: 0

N. J. A. Sloane, May 09 2005

"There are 94343 inequivalent doubly even self-dual codes of length 40, 16470 of which are extremal" [Betsumiya et al.] - Jonathan Vos Post, Aug 06 2012

Koichi Betsumiya, Masaaki Harada and Akihiro Munemasa, A Complete Classification of Doubly Even Self-Dual Codes of Length 40, arXiv:1104.3727v3 [math.CO], v3, Aug 02, 2012. - From _Jonathan Vos Post_, Aug 06 2012
J. H. Conway and V. S. Pless, On the enumeration of self-dual codes, J. Comb. Theory, A28 (1980), 26-53. [DOI] MR0558873
J. H. Conway, V. Pless and N. J. A. Sloane, The Binary Self-Dual Codes of Length Up to 32: A Revised Enumeration, J. Comb. Theory, A60 (1992), 183-195 (Abstract, pdf, ps, Table A, Table D).
W. C. Huffman, On the classification and enumeration of self-dual codes, Finite Fields Applic. 11 (2005), 451-490. [DOI]
G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
V. S. Pless, The children of the (32,16) doubly even codes, IEEE Trans. Inform. Theory, 24 (1978), 738-746. [DOI] MR0514353
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. A003178, A003179, A106162, A106163, A106164, A106165, A106166, A106167, A215219.

A106165 Number of inequivalent (indecomposable or decomposable) Type I but not Type II binary self-dual codes of length 2n.

Original entry on oeis.org

0, 1, 1, 1, 1, 2, 3, 4, 5, 9, 16, 25, 46, 103, 261, 731, 3210, 24147

Offset: 0

N. J. A. Sloane, May 09 2005, Aug 23 2008

The minimal distance of these codes is not constrained. A105685 gives the number with the highest minimal distance.

R. T. Bilous and G. H. J. van Rees, An enumeration of binary self-dual codes of length 32, Designs, Codes Crypt., 26 (2002), 61-86.
J. H. Conway and V. S. Pless, On the enumeration of self-dual codes, J. Comb. Theory, A28 (1980), 26-53. MR0558873
J. H. Conway, V. Pless and N. J. A. Sloane, The Binary Self-Dual Codes of Length Up to 32: A Revised Enumeration, J. Comb. Theory, A28 (1980), 26-53 (Abstract, pdf, ps, Table A, Table D).
W. C. Huffman, On the classification and enumeration of self-dual codes, Finite Fields Applic., 11 (2005), 451-490.
G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
V. S. Pless, The children of the (32,16) doubly even codes, IEEE Trans. Inform. Theory, 24 (1978), 738-746.
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. A003178, A003179, A106162-A106167.

A106164 Number of indecomposable Type I but not Type II binary self-dual codes of length 2n.

Original entry on oeis.org

0, 1, 0, 0, 0, 0, 1, 1, 1, 2, 6, 8, 19, 45, 148, 457, 2448, 20786

Offset: 0

N. J. A. Sloane, May 09 2005

R. T. Bilous, Enumeration of binary self-dual codes of length 34, Preprint, 2005.
R. T. Bilous and G. H. J. van Rees, An enumeration of binary self-dual codes of length 32, Designs, Codes Crypt., 26 (2002), 61-86.
J. H. Conway and V. S. Pless, On the enumeration of self-dual codes, J. Comb. Theory, A28 (1980), 26-53.
V. S. Pless, The children of the (32,16) doubly even codes, IEEE Trans. Inform. Theory, 24 (1978), 738-746.

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
J. H. Conway, V. Pless and N. J. A. Sloane, The Binary Self-Dual Codes of Length Up to 32: A Revised Enumeration, J. Comb. Theory, A28 (1980), 26-53 (Abstract, pdf, ps, Table A, Table D).
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. A003178, A003179, A106162-A106167.

a(34) computed by N. J. A. Sloane, based on data in Bilous's paper, Sep 06 2005

A215219 Number of (indecomposable or decomposable) Type II binary self-dual codes of length 8n with the highest minimal distance.

Original entry on oeis.org

1, 1, 2, 1, 5, 16470, 1

Offset: 0

N. J. A. Sloane, Aug 08 2012

nonn

It is important to distinguish between "extremal" (meaning having the highest possible minimal distance permitted by Gleason's theorem) and "optimal" (meaning having the highest minimal distance that can actually be achieved). This sequence enumerates optimal codes. Extremal codes do not exist when n is sufficiently large. For lengths up to at least 64, "extremal" and "optimal" coincide.

"There are 94343 inequivalent doubly even self-dual codes of length 40, 16470 of which are extremal." [Betsumiya et al.] - Jonathan Vos Post, Aug 06 2012

Koichi Betsumiya, Masaaki Harada and Akihiro Munemasa, A Complete Classification of Doubly Even Self-Dual Codes of Length 40, arXiv:1104.3727v3 [math.CO], v3, Aug 02, 2012. - From _Jonathan Vos Post_, Aug 06 2012
J. H. Conway and V. S. Pless, On the enumeration of self-dual codes, J. Comb. Theory, A28 (1980), 26-53. [DOI] MR0558873
J. H. Conway, V. Pless and N. J. A. Sloane, The Binary Self-Dual Codes of Length Up to 32: A Revised Enumeration, J. Comb. Theory, A60 (1992), 183-195 (Abstract, pdf, ps, Table A, Table D).
S. K. Houghten, C. W. H. Lam, L. H. Thiel and J. A. Parker, The extended quadratic residue code is the only (48,24,12) self-dual doubly-even code, IEEE Trans. Inform. Theory, 49 (2003), 53-59.
W. C. Huffman, On the classification and enumeration of self-dual codes, Finite Fields Applic. 11 (2005), 451-490. [DOI]
G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
V. S. Pless, The children of the (32,16) doubly even codes, IEEE Trans. Inform. Theory, 24 (1978), 738-746. [DOI] MR0514353
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. A003178, A003179, A106162-A106167.

a(6) = 1 (due to Houghten et al.) from Akihiro Munemasa, Aug 08 2012

A110193 Number of (indecomposable or decomposable) binary self-dual codes (singly- or doubly-even) of length 2n and minimal distance exactly 6.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 3, 13, 74, 938

Offset: 1

N. J. A. Sloane, Sep 06 2005

nonn

In fact all such codes of length <= 42 are indecomposable.

R. T. Bilous, Enumeration of binary self-dual codes of length 34, Preprint, 2005.
R. T. Bilous and G. H. J. van Rees, An enumeration of binary self-dual codes of length 32, Designs, Codes Crypt., 26 (2002), 61-86.
J. H. Conway and V. S. Pless, On the enumeration of self-dual codes, J. Comb. Theory, A28 (1980), 26-53.
V. S. Pless, The children of the (32,16) doubly even codes, IEEE Trans. Inform. Theory, 24 (1978), 738-746.

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
J. H. Conway, V. Pless and N. J. A. Sloane, The Binary Self-Dual Codes of Length Up to 32: A Revised Enumeration, J. Comb. Theory, A28 (1980), 26-53 (Abstract, pdf, ps, Table A, Table D).
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. A003179, A106167.

cp's OEIS Frontend

A106162 Number of indecomposable Type II binary self-dual codes of length 8n.

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A106163 Total number of (indecomposable or decomposable) Type II binary self-dual codes of length 8n.

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A106165 Number of inequivalent (indecomposable or decomposable) Type I but not Type II binary self-dual codes of length 2n.

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A106164 Number of indecomposable Type I but not Type II binary self-dual codes of length 2n.

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A215219 Number of (indecomposable or decomposable) Type II binary self-dual codes of length 8n with the highest minimal distance.

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A110193 Number of (indecomposable or decomposable) binary self-dual codes (singly- or doubly-even) of length 2n and minimal distance exactly 6.

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