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 1-4 of 4 results.

A057608 Maximal size of binary code of length n that corrects one transposition (end-around transposition not included).

Original entry on oeis.org

1, 2, 3, 4, 8, 12, 20, 38, 63, 110, 196, 352
Offset: 0

Views

Author

N. J. A. Sloane, Oct 09 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. A057657, A000016, A057591, A010101. Row sums of A085684.

Extensions

a(9) = 110 from Butenko et al., Nov 28 2001 (see reference).
a(9) = 110 also from Ketan Narendra Patel (knpatel(AT)eecs.umich.edu), Apr 29 2002. Confirmed by N. J. A. Sloane, Jul 07 2003
a(10) >= 196 and a(11) >= 352 from Butenko et al., Nov 28 2001 (see reference).
a(10) = 196 found by N. J. A. Sloane, Jul 17 2003
a(11) = 352 proved by Brian Borchers (borchers(AT)nmt.edu), Oct 16 2009

A010336 Maximal size of binary code of length n and asymmetric distance 5.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 2, 2, 2, 4, 4, 4, 6, 8, 12, 16, 26
Offset: 1

Views

Author

N. J. A. Sloane, Apr 10 2000

Keywords

References

  • T. Etzion, New lower bounds for asymmetric and unidirectional codes, IEEE Trans. Inform. Theory, 37 (1991), 1696-1705.
  • J. H. Weber, Bounds and Constructions for Binary Block Codes Correcting Asymmetric or Unidirectional Errors, Ph. D. Thesis, Tech. Univ. Delft, 1989.
  • J. H. Weber, C. de Vroedt and D. E. Boekee, Bounds and constructions for binary codes of length less than 24 and asymmetric distance less than 6, IEEE Trans. Inform. Theory, 34 (1988), 1321-1332.

Crossrefs

Cf. A010101, A010238, A054536.

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

A054536 Maximal size of binary code of length n and asymmetric distance 4.

Original entry on oeis.org

1, 1, 1, 2, 2, 4, 2, 4, 4, 6, 8, 12, 18
Offset: 1

Views

Author

N. J. A. Sloane, Apr 10 2000

Keywords

Links

Crossrefs

Cf. A010101, A010238, A010336.
Showing 1-4 of 4 results.

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

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