cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A076834 Number of inequivalent projective binary linear [n,k] codes of any dimension k <= n. Also the number of simple binary matroids on n points.

Original entry on oeis.org

1, 1, 2, 3, 5, 10, 20, 42, 102, 276, 857, 3233, 15113, 91717, 751479
Offset: 1

Views

Author

N. J. A. Sloane, Nov 21 2002

Keywords

Comments

A code is projective if all columns are distinct and nonzero.

References

  • H. Fripertinger and A. Kerber, in AAECC-11, Lect. Notes Comp. Sci. 948 (1995), 194-204.
  • D. Slepian, Some further theory of group codes. Bell System Tech. J. 39 1960 1219-1252.
  • M. Wild, Enumeration of binary and ternary matroids and other applications of the Brylawski-Lucas Theorem, Preprint Nr. 1693, Tech. Hochschule Darmstadt, 1994

Links

Crossrefs

Row sums of A076833. A diagonal of A091008.

Extensions

More terms from Marcel Wild, Nov 26 2002

A076833 Triangle T(n,k) read by rows giving number of inequivalent projective binary linear [n,k] codes (n >= 1, 1 <= k <= n).

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 0, 1, 3, 1, 0, 0, 1, 4, 4, 1, 0, 0, 1, 5, 8, 5, 1, 0, 0, 0, 6, 15, 14, 6, 1, 0, 0, 0, 5, 29, 38, 22, 7, 1, 0, 0, 0, 4, 46, 105, 80, 32, 8, 1, 0, 0, 0, 3, 64, 273, 312, 151, 44, 9, 1, 0, 0, 0, 2, 89, 700, 1285, 821, 266, 59, 10, 1, 0, 0, 0, 1, 112
Offset: 1

Views

Author

N. J. A. Sloane, Nov 21 2002

Keywords

Comments

A code is projective if all columns are distinct and nonzero.

Examples

			1; 0,1; 0,1,1; 0,0,2,1; 0,0,1,3,1; 0,0,1,4,4,1; 0,0,1,5,8,5,1; ...

References

  • D. Slepian, Some further theory of group codes. Bell System Tech. J. 39 1960 1219-1252.
  • H. Fripertinger and A. Kerber, in AAECC-11, Lect. Notes Comp. Sci. 948 (1995), 194-204.

Links

Crossrefs

Cf. A076834 (row sums). Partial sums across rows gives triangle A091008.
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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