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

Rama Asad

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

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Volume 3 • Issue 2 • PP: 25-39 • 2023

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

Rama Asad Nadweh ^1*

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¹Online Islamic University, Department Of Science and Information Technology, Doha, Qatar

* Corresponding Author.

DOI https://doi.org/10.54216/PMTCS.030202

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

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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.

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Nadweh, Rama Asad. "Linear Codes over Finite Fields Based On Greedy Algorithms and Their Applications." Pure Mathematics for Theoretical Computer Science, vol. Volume 3, no. Issue 2, 2023, pp. 25-39. DOI: https://doi.org/10.54216/PMTCS.030202

Nadweh, R. (2023). Linear Codes over Finite Fields Based On Greedy Algorithms and Their Applications. Pure Mathematics for Theoretical Computer Science, Volume 3(Issue 2), 25-39. DOI: https://doi.org/10.54216/PMTCS.030202

Nadweh, Rama Asad. "Linear Codes over Finite Fields Based On Greedy Algorithms and Their Applications." Pure Mathematics for Theoretical Computer Science Volume 3, no. Issue 2 (2023): 25-39. DOI: https://doi.org/10.54216/PMTCS.030202

Nadweh, R. (2023) 'Linear Codes over Finite Fields Based On Greedy Algorithms and Their Applications', Pure Mathematics for Theoretical Computer Science, Volume 3(Issue 2), pp. 25-39. DOI: https://doi.org/10.54216/PMTCS.030202

Nadweh R. Linear Codes over Finite Fields Based On Greedy Algorithms and Their Applications. Pure Mathematics for Theoretical Computer Science. 2023;Volume 3(Issue 2):25-39. DOI: https://doi.org/10.54216/PMTCS.030202

R. Nadweh, "Linear Codes over Finite Fields Based On Greedy Algorithms and Their Applications," Pure Mathematics for Theoretical Computer Science, vol. Volume 3, no. Issue 2, pp. 25-39, 2023. DOI: https://doi.org/10.54216/PMTCS.030202

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