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.

Showing 1-3 of 3 results.

A057657 Maximal size of binary code of length n that corrects one transposition (end-around transposition included).

Original entry on oeis.org

2, 3, 4, 5, 8, 18, 28, 50, 100, 171, 316
Offset: 1

Views

Author

N. J. A. Sloane, Oct 15 2000

Keywords

References

  • S. Butenko, P. Pardalos, I. Sergienko, V. P. Shylo and P. Stetsyuk, Estimating the size of correcting codes using extremal graph problems, Optimization, 227-243,
  • Springer Optim. Appl., 32, Springer, New York, 2009.
  • N. J. A. Sloane, On single-deletion-correcting codes, in Codes and Designs (Columbus, OH, 2000), 273-291, Ohio State Univ. Math. Res. Inst. Publ., 10, de Gruyter, Berlin, 2002.

Links

Crossrefs

Cf. A057608, A000016, A057591. Row sums of A085685.

Extensions

Typo in a(8) corrected and a(9) added, Jul 09 2003
a(9) = 100 from Butenko et al., Nov 28 2001 (see reference). Confirmed by N. J. A. Sloane, Jul 09 2003
a(10) >= 171 and a(100) >= 316 from Butenko et al., Nov 28 2001 (see reference).
a(10) = 171 from Brian Borchers (borchers(AT)nmt.edu), Apr 14 2005
a(11) = 316 from Brian Borchers (borchers(AT)nmt.edu), Nov 04 2009

A057591 Maximal size of binary code of length n that corrects 2 deletions.

Original entry on oeis.org

1, 1, 2, 2, 2, 4, 5, 7, 11, 16, 24
Offset: 1

Views

Author

N. J. A. Sloane, Oct 05 2000

Keywords

Comments

Comments from Pablo San Segundo, Dec 04 2015 (Start): The search for a maximal clique in the graph 2dc.2048 has now finished. The answer is 24 (which was already known to be a lower bound).
The total time was 16.4 days using a 20-core XEON with 128Gb. 18 cores out of the 20 were in fact used.
The solution was found by a strong heuristic algorithm during pre-processing (about 5s). The actual search time was used "only" to prove optimality. The actual maximum clique algorithm is our most recent variant based on infra-chromatic BBMCX, described here, but as yet unpublished: https://www.researchgate.net/profile/Pablo_San_Segundo
The project was carried out by Pablo San Segundo and Jorge Artieda, Polytechnic University of Madrid (UPM), Center of Automation and Robotics (CAR). Supported by National Grant DPI 2014-53525-C3-1-R (End)

Links

Crossrefs

Cf. A000016, A057608, A057657, A010101.

Extensions

Guenter Stertenbrink (Sterten(AT)aol.com) found a(9) = 11 and a(10) >= 16, Apr 28 2001
James B. Shearer (jbs(AT)pkmfgvm4.vnet.ibm.com) proved that a(10) = 16, Sep 20 2003
Pablo San Segundo and Jorge Artieda showed that a(11) = 24, Dec 04 2015

A085684 Triangle read by rows: T(n,k), n >= 0, 0 <= k <= n, is size of maximal 1-transposition-correcting code formed using binary vectors of length n and weight k.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 3, 3, 2, 1, 1, 2, 4, 6, 4, 2, 1, 1, 3, 6, 9, 9, 6, 3, 1, 1, 3, 7, 13, 15, 13, 7, 3, 1, 1, 3, 9, 18, 24, 24, 18, 9, 3, 1, 1, 4, 11, 24, 37, 42, 37, 24, 11, 4, 1
Offset: 0

Views

Author

N. J. A. Sloane, Jul 17 2003

Keywords

Examples

			Triangle begins
1
1 1
1 1 1
1 1 1 1
1 2 2 2 1
1 2 3 3 2 1
1 2 4 6 4 2 1

Links

Crossrefs

Column k=1 is floor(n/3), column k=2 is A085680, row sums are A057608.
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.