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Pure Mathematics for Theoretical Computer Science

Volume 3 , Issue 2 , PP: 25-39, 2023 | Cite this article as | XML | Html | PDF | Full Length Article

Linear Codes over Finite Fields Based On Greedy Algorithms and Their Applications

Rama Asad Nadweh 1

  • 1 Online Islamic University, Department Of Science and Information Technology, Doha, Qatar - (ramaanadwehh@gmail.com)

    • Doi: https://doi.org/10.54216/PMTCS.030202

    Received: June 11, 2023 Revised: September 24, 2023 Accepted: December 17, 2023
    Abstract

    In this paper we prove that for any ordered basis  of a vector space there is a basis  for which the greedy code generated using the B-ordering is linear with respect to , where B2 is derived from  by a lower triangular matrix P; . In Addition we prove a similar result for self-orthogonal greedy codes.

    Keywords :

    greedy algorithm , finite field , linear codes , coding theory

    References

    [1]    Mohammed El-Atrash, "Greedy codes over Zp", Journal of AlHadbaa University College, (2000).

    [2]    Mohammed El-Atrash, "Linearity of binary greedy codes", Islamic University Journal, (2000) Vol. 8 No. 2, part 2.

    [3]    Mohammed El-Atrash, et. El. "Linear codes over the ring Z4 using almost greedy algorithm", Islamic University Journal, (2003) Vol. 11 No. 1.

    [4]    J.H. Conway and N.J.A. Sloane, "Lexicographic Codes: Error Correcting Codes from Game Theory", IEEE Trans. Inform. Theory IT-32 (1986), 337-348.

    [5]    Richard Brualdi and Verra Pless, "Greedy Codes", JCT (A) 64 (1993).

    [6]    Monroe, Laura, "Binary Greedy Codes", to appear in Congressus Numerantium, vol. 100-104.

    Cite This Article As :
    Asad, Rama. Linear Codes over Finite Fields Based On Greedy Algorithms and Their Applications. Pure Mathematics for Theoretical Computer Science, vol. , no. , 2023, pp. 25-39. DOI: https://doi.org/10.54216/PMTCS.030202
    Asad, R. (2023). Linear Codes over Finite Fields Based On Greedy Algorithms and Their Applications. Pure Mathematics for Theoretical Computer Science, (), 25-39. DOI: https://doi.org/10.54216/PMTCS.030202
    Asad, Rama. Linear Codes over Finite Fields Based On Greedy Algorithms and Their Applications. Pure Mathematics for Theoretical Computer Science , no. (2023): 25-39. DOI: https://doi.org/10.54216/PMTCS.030202
    Asad, R. (2023) . Linear Codes over Finite Fields Based On Greedy Algorithms and Their Applications. Pure Mathematics for Theoretical Computer Science , () , 25-39 . DOI: https://doi.org/10.54216/PMTCS.030202
    Asad R. [2023]. Linear Codes over Finite Fields Based On Greedy Algorithms and Their Applications. Pure Mathematics for Theoretical Computer Science. (): 25-39. DOI: https://doi.org/10.54216/PMTCS.030202
    Asad, R. "Linear Codes over Finite Fields Based On Greedy Algorithms and Their Applications," Pure Mathematics for Theoretical Computer Science, vol. , no. , pp. 25-39, 2023. DOI: https://doi.org/10.54216/PMTCS.030202

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