research-article

Improved upper bounds on sizes of codes

Authors:

B. Mounits,

T. Etzion,

S. LitsynAuthors Info & Claims

IEEE Transactions on Information Theory, Volume 48, Issue 4

Pages 880 - 886

https://doi.org/10.1109/18.992776

Published: 01 September 2006 Publication History

Abstract

Let A(n,d) denote the maximum possible number of codewords in a binary code of length n and minimum Hamming distance d. For large values of n, the best known upper bound, for fixed d, is the Johnson bound. We give a new upper bound which is at least as good as the Johnson bound for all values of n and d, and for each d there are infinitely many values of n for which the new bound is better than the Johnson bound. For small values of n and d, the best known method to obtain upper bounds on A(n,d) is linear programming. We give new inequalities for the linear programming and show that with these new inequalities some of the known bounds on A(n,d) for n&les;28 are improved

Cited By

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Tseng PLai CYu W(2023)Semidefinite programming bounds for binary codes from a split Terwilliger algebraDesigns, Codes and Cryptography10.1007/s10623-023-01250-491:10(3241-3262)Online publication date: 9-Jun-2023
https://dl.acm.org/doi/10.1007/s10623-023-01250-4
Tseng PLai CYu W(2022)Improved semidefinite programming bounds for binary codes by split distance enumerations2022 IEEE International Symposium on Information Theory (ISIT)10.1109/ISIT50566.2022.9834515(3073-3078)Online publication date: 26-Jun-2022
https://dl.acm.org/doi/10.1109/ISIT50566.2022.9834515
Kou YHu XYang W(2021)The clique distribution in powers of hypercubesDiscrete Applied Mathematics10.1016/j.dam.2021.08.030305:C(76-85)Online publication date: 31-Dec-2021
https://dl.acm.org/doi/10.1016/j.dam.2021.08.030
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Index Terms

Improved upper bounds on sizes of codes
1. Mathematics of computing
  1. Mathematical analysis
    1. Mathematical optimization
      1. Continuous optimization
        Linear programming
2. Theory of computation
  1. Design and analysis of algorithms
    1. Mathematical optimization
      1. Continuous optimization
        Linear programming

Index terms have been assigned to the content through auto-classification.

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IEEE Transactions on Information Theory Volume 48, Issue 4

April 2002

208 pages

ISSN:0018-9448

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IEEE Press

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Published: 01 September 2006

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Tseng PLai CYu W(2023)Semidefinite programming bounds for binary codes from a split Terwilliger algebraDesigns, Codes and Cryptography10.1007/s10623-023-01250-491:10(3241-3262)Online publication date: 9-Jun-2023
https://dl.acm.org/doi/10.1007/s10623-023-01250-4
Tseng PLai CYu W(2022)Improved semidefinite programming bounds for binary codes by split distance enumerations2022 IEEE International Symposium on Information Theory (ISIT)10.1109/ISIT50566.2022.9834515(3073-3078)Online publication date: 26-Jun-2022
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Kou YHu XYang W(2021)The clique distribution in powers of hypercubesDiscrete Applied Mathematics10.1016/j.dam.2021.08.030305:C(76-85)Online publication date: 31-Dec-2021
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Laaksonen Astergrd P(2017)Constructing error-correcting binary codes using transitive permutation groupsDiscrete Applied Mathematics10.1016/j.dam.2017.08.022233:C(65-70)Online publication date: 31-Dec-2017
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Martin WTanaka H(2009)Commutative association schemesEuropean Journal of Combinatorics10.1016/j.ejc.2008.11.00130:6(1497-1525)Online publication date: 1-Aug-2009
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Nonasymptotic Upper Bounds for Deletion Correcting Codes

New upper bounds on Lee codes

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