College of Education for Pure Science

Master Thesis Viva in the College of Education for Pure Science entitled ” New Applications of Coding Theory in theProjective  Space of Order Eight”

The College of Education for Pure Science, University of Mosul, has done the Master Thesis Viva entitled ” New Applications of Coding Theory in theProjective  Space of Order Eight”

On Thursday, June 22, 2023, the College staff including the respected Dean of the College, Assistant Professor Dr. Qais Ismail Ibrahim, the Honorable Scientific Associate and Administrative Associate, the Honorable Head of the Department of Mathematics, and a number of the college’s teachers were attended the viva

This study, presented by the Master student Marwa Hussein Rajab in the Department of Mathematics, aims to correct the errors of the codes that are formed and establish the relationship between the applications of the coding theory in the projective plane PG(2,8) of the eighth order and to study the applications of the coding theory in the projective space PG(3,8) on the Galois field of the eighth order in the linear projection ( n, k. d, q) as the code length n and then calculate the code dimensions k and the minimum distance d with error correction e according to the hit matrix. This thesis also presents examples and theories of the links between combinatorial structures and coding theory. Also, the coding theory was applied to the plane and projective space, and we found the parameters and noticed that they are not ideal. Finally, the aim of this work is to build complete surfaces and arches in the three-dimensional projective space PG (3,8) over Galois fields 8 = q, which represents the application of algebraic geometry in the three – dimensional projective space PG(3,8), where 8 = q, which is the  (k,Ɬ) – span in PG (3,8). The results were as follows: first we found the points, lines and planes in space and constructed the (k,Ɬ) – span which is a set of k lines that no two of them intersect. The maximum whole area of the (k,Ɬ) – span in PG(3,8) is (65, Ɬ ) which is equal to all the points it intersects and equals an empty set called the spreads. Each point in space is an element of the spreads and satisfies the equation q2+1

The Viva committee was chaired by Prof. Dr. Ammar Seddiq Mahmood / University of Mosul, College of Education for Pure Science and the membership of Asst. Prof. Zubaida Mohammed Ibrahee / University of Mosul, College of Computer Sciences and Mathematics, Asst. Prof. Dr. Herish Omer Abdullah, Salahddin University – Erbil , College of Sciences, and  under the supervision and membership of Prof. Dr. Nada Yassen  Kasm Yahya, University of Mosul, College of Education for Pure Science.

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