Applications of the  PG(5,q)  in coding theory

Yahya ammar fawzy  yahya; Nada yassen kasm  yahya

doi:10.24996/ijs.2025.66.11.25

Authors

Yahya ammar fawzy yahya Department of mathematics, College Computer sciences and mathematics, University of Mosul, City Nineveh, Country Iraq https://orcid.org/0009-0000-9739-0823
Nada yassen kasm yahya Department of mathematics, College of education for pure science, University of mosul, City Nineveh, Country Iraq

DOI:

https://doi.org/10.24996/ijs.2025.66.11.25

Keywords:

Finite projective space, incidence matrix, linear code, PG(5,q), perfect

Abstract

This paper's primary goal is to present the connection between coding theory and the projective space PG(5,q) of order q, where q={2,3,4,5,7,8,9,11} It was determined whether or not the [n,k,d]-code is perfect. Where n is the length of the code, k is the code dimension, and d is the minimum distance, were calculated with error correction e according to the incidence matrix. We have found that the [n,k,d]-code in PG(5,q), q= {2,3,4,5,7,8,9,11}, is perfect if e = 1.

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Published

2025-11-30

Issue

Vol 66 No 11 (2025)

Section

Mathematics

License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

[1]

Y. ammar fawzy . yahya and N. yassen kasm . yahya, “Applications of the PG(5,q) in coding theory”, Iraqi Journal of Science, vol. 66, no. 11, pp. 5002–5014, Nov. 2025, doi: 10.24996/ijs.2025.66.11.25.