호남수학학술지 (Honam Mathematical Journal)

  • 제30권1호
  • /
  • Pages.33-45
  • /
  • 2008
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

SIMULTANEOUS RANDOM ERROR CORRECTION AND BURST ERROR DETECTION IN LEE WEIGHT CODES

  • Jain, Sapna (Department of Mathematics, University of Delhi)
  • 투고 : 2007.09.19
  • 심사 : 2008.01.04
  • 발행 : 2008.03.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Lee weight is more appropriate for some practical situations than Hamming weight as it takes into account magnitude of each digit of the word. In this paper, we obtain a sufficient condition over the number of parity check digits for codes correcting random errors and simultaneously detecting burst errors with Lee weight consideration.

키워드

참고문헌

  1. E.R. Berlekamp, Algebraic Coding Theory, McGraw Hill, New York, 1968.
  2. C.N. Campopiano, Bounds on Burst Error Correcting Codes, IRE. Trans., IT-8 (1962), 257-259.
  3. E.N. Gilbert, A Comparison of signaling alphabets, Bell System Tech. J., 31 (1952), 504-522. https://doi.org/10.1002/j.1538-7305.1952.tb01393.x
  4. E.N. Gilbert, Capacity of a burst-noise channel, Bell System Tech. J., 39 (1960), 1253-1265. https://doi.org/10.1002/j.1538-7305.1960.tb03959.x
  5. W. Cary Huffman and Vera Pless, Fundamentals of Error-Correcting Codes, Cambridge University Press, 2003.
  6. S. Jain, Modification to a Bound for Random error Correction with Lee Weight, Communications of the Korean Mathematical Society, 20 (2005), 405-409. https://doi.org/10.4134/CKMS.2005.20.2.405
  7. S. Jain, K-B.Nam and K-S. Lee, On Some Perfect Codes with respect to Lee Metric, Linear Algebra and Its Applications, 405 (2005), 104-120. https://doi.org/10.1016/j.laa.2005.03.001
  8. S. Jain, Error Detecting and Error Correcting Capabilities of Euclidean Codes, Ed. Vol.: Pragmatic Algebra, Eds.: Ki-Bong Nam et al., 2006, pp.51-66.
  9. S. Jain, Varshamov-Gilbert-Sacks Bound for Linear Lee Weight Codes, to appear in Algebras, Groups, Geometries.
  10. S. Jain and K.P. Shum, Sufficient Condition over the Number of Parity Checks for Burst Error Detection/Correction in Linear Lee Weight Codes, Algebra Colloquium, 14 (2007), 341-350. https://doi.org/10.1142/S1005386707000338
  11. S. Jain and Ki-Bong Nam, Lower Bounds for Codes Correcting Moderate-Density Bursts of Fixed Length with Lee Weight Consideration, Linear Algebra and Its Applications, 418 (2006), 122-129. https://doi.org/10.1016/j.laa.2006.01.021
  12. M.L. Kaushik, Necessary and Sufficient Number of Parity Checks in Codes Correcting Random Errors and Bursts with Weight Constraints under a New Metric, Information Sciences, 19 (1979), 81-90. https://doi.org/10.1016/0020-0255(79)90033-1
  13. C.Y. Lee, Some properties of non-binary error correcting codes, IEEE Trans. Information Theory, IT-4 (1958), 77-82.
  14. W.W. Peterson and E.J. Weldon, Error Correcting Codes, 2nd Edition, MIT Press, Cambridge, Massachusetts, 1972.
  15. G.E. Sacks, Multiple error correction by means of parity-checks, IRE Trans. Informations Theory, IT-4, 1958, 145-147.
  16. B.D. Sharma and B.K. Dass, On linear codes correcting random and low-density burst errors, Linear Algebra and Its Applications, 16 (1977), 5-18. https://doi.org/10.1016/0024-3795(77)90014-3
  17. B.D. Sharma and S.N. Goel, A Note on Bounds for Burst Correcting Codes with Lee Weight Consideration, Information and Control, 33 (1977), 210-216. https://doi.org/10.1016/S0019-9958(77)80002-8
  18. A.D. Wyner, Low-density-burst-correcting Codes, IEEE. Trans. Information Theory, IT-9 (1963), 124. https://doi.org/10.1109/TIT.1963.1057819

피인용 문헌

  1. Extended Varshamov-Gilbert-Sacks Bound for Linear Lee Weight Codes vol.19, pp.spec01, 2012, https://doi.org/10.1142/S1005386712000752
  2. Construction of Lee Weight Codes Detecting CT-Burst Errors and Correcting Random Errors vol.18, pp.spec01, 2011, https://doi.org/10.1142/S1005386711000733