본문 바로가기
KERD
논문KCI 등재

A simple proof of the improved Johnson bound for binary codes

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

In this paper, we give a simple proof of the improved Johnson bound for $A(n,d)$, the maximum number of codewords in a binary code of length $n$ and minimum distance $d$, given by Mounits, Etzion and Litsyn.

Abstract

In this paper, we give a simple proof of the improved Johnson bound for $A(n,d)$, the maximum number of codewords in a binary code of length $n$ and minimum distance $d$, given by Mounits, Etzion and Litsyn.

참고문헌 (22)

  1. E. Agrell, "A table of upper bounds for binary codes", IEEE Trans. Inform. Theory, 47(7), pp.3004~3006 (2001)
  2. J. Bao, "The completion determination of optimal (3,4)-packings", Des. Codes Cryptogr, 77(1), pp.217~229 (2015)
  3. M. R. Best, "Binary codes with a minimum distance of four", IEEE Trans. Inform. Theory, 26(6), pp.738~742 (1980)
  4. G. Cohen, "Covering Codes" (1997), North-Holland Publishing Co.
  5. P. Delsarte, "An algebraic approach to the association schemes of coding theory", Philips Res. Rep. Suppl, (10), pp.vi+97~ (1973)
  6. K. Elssel, "Two new nonlinear binary codes", IEEE Trans. Inform. Theory, 51(3), pp.1189~1190 (2005)
  7. D. C. Gijswijt, "Semidenite code bounds based on quadruple distances", IEEE Trans. Inform. Theory, 58(5), pp.2697~2705 (2012)
  8. W. Haas, "On the failing cases of the Johnson bound for error-correcting codes", Electron. J. Combin, 15(1), pp.13~ (2008)[DOI]
  9. S. M. Johnson, "A new upper bound for error-correcting codes", IRE Trans, IT-8, pp.203~207 (1962)
  10. M. K. Kaikkonen, "A new four-error-correcting code of length 20", IEEE Trans. Inform. Theory, 35(6), pp.1344~
  11. M. K. Kaikkonen, "Codes from ane permutation groups", Des. Codes Cryptogr, 15(2), pp.183~186 (1998)
  12. H. K. Kim, "Improved semidenite programming bound on sizes of codes", IEEE Trans. Inform. Theory, 59(11), pp.7337~7345 (2013)
  13. Y. Klein, "Two new bounds on the size of binary codes with a minimum distance of three", Des. Codes Cryptogr, 6(3), pp.219~227 (1995)
  14. A. Laaksonen, "Constructing error-correcting binary codes using transitive permutation groups", Discrete Appl. Math, 233, pp.65~70 (2017)
  15. F. J. MacWilliams, "The Theory of Error-Correcting Codes. I" (1977), North-Holland Publishing Co.
  16. M. Milshtein, "A new binary code of length 16 and minimum distance 3", Inform. Process. Lett, 115(12), pp.975~976 (2015)
  17. B. Mounits, "Improved upper bounds on sizes of codes", IEEE Trans. Inform. Theory, 48(4), pp.880~886 (2002)
  18. B. Mounits, "New upper bounds on codes via association schemes and linear programming", Adv. Math. Commun, 1(2), pp.173~195 (2007)
  19. P. R. J. Ostergard, "Two new four-error-correcting binary codes", Des. Codes Cryptogr, 36(3), pp.327~329 (2005)
  20. P. R. J. Ostergard, "On optimal binary codes with unbalanced coordinates", Appl. Algebra Engrg. Comm. Comput, 24(3-4), pp.197~200 (2013)
  21. P. R. J. Ostergard, "Optimal binary one-error-correcting codes of length 10 have 72 codewords", IEEE Trans. Inform. Theory, 45(4), pp.1229~1231 (1999)
  22. A. Schrijver, "New code upper bounds from the Terwilliger algebra and semidenite pro-gramming", IEEE Trans. Inform. Theory, 51(8), pp.2859~2866 (2005)

관련 논문AI추천

이 간행물의 다른 논문 (25건)