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.

Previous Showing 21-23 of 23 results.

A136725 Primitive dimensions of Hadamard matrices.

Original entry on oeis.org

1, 2, 12, 20, 28, 36, 44, 52, 60, 68, 76, 84, 92, 100
Offset: 1

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Author

Artur Jasinski, Jan 19 2008

Keywords

Comments

In primitive dimensions, Hadamard matrices cannot be obtained as tensor products of Hadamard matrices of lower dimensions.

Links

Crossrefs

Cf. A007299, A136724.

A147774 Number of equivalence classes of normalized Hadamard matrices of order 4n with respect to permutations of rows and columns.

Original entry on oeis.org

1, 1, 2, 118, 6520, 43966313
Offset: 1

Views

Author

Alexander Adamchuk, Nov 12 2008

Keywords

Comments

Number of equivalence classes N(k) = {1, 1, 1, 1, 2, 118, 6520, 43966313} for order k = {1, 2, 4, 8, 12, 16, 20, 24}, (see Theorem 2 at the Hadamard matrices project results link). Note that N(24) = a(6) = 43966313 is a prime.

Links

Crossrefs

Cf. A007299 = Number of Hadamard matrices of order 4n.

A158865 Smallest maximal excess attained by an equivalence class of Hadamard matrices of order 4n.

Original entry on oeis.org

0, 8, 20, 36, 56, 80, 108, 140
Offset: 0

Views

Author

William P. Orrick, Mar 28 2009

Keywords

Comments

The excess of a {-1,1} matrix is the sum of its elements. The maximal excess of an equivalence class of Hadamard matrices (cf. A007299) is the largest excess attained by a member of the class. The largest maximal excess of any equivalence class is given by A004118.

Examples

			All equivalence classes in orders 20 and 28 attain the same maximal excess. In order 16, three classes attain maximal excess 64 and two attain maximal excess 56. In order 24, 56 equivalence classes attain maximal excess 112 and four attain maximal excess 108.

References

  • Best, M. R. The excess of a Hadamard matrix. Nederl. Akad. Wetensch. Proc. Ser. A {80}=Indag. Math. 39 (1977), no. 5, 357-361.
  • Brown, Thomas A. and Spencer, Joel H., Minimization of +-1 matrices under line shifts. Colloq. Math. 23 (1971), 165-171, 177 (errata).
  • R. Craigen and H. Kharaghani, Weaving Hadamard matrices with maximum excess and classes with small excess. J. Combinatorial Designs 12 (2004), 233-255.

Formula

For bounds on a(n), see A004118.
Previous Showing 21-23 of 23 results.

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