College of Education for Pure Science

Master Thesis Viva in the College of Education for Pure Science entitled ” New Results for Construction Codes raised from (k , ℓ) – span in PG(3,17)”

The College of Education for Pure Science, University of Mosul, has done the Master Thesis Viva entitled ” New Results for Construction Codes raised from (k , ℓ) – span in PG(3,17)”,

On Sunday, July 9, 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.

The aim of this study, presented by the Master student Dakheel Abdulqader Elias in the Department of Mathematics, is to construct codes arising from complete k – span where K = q2 – n q +1 in PG (3,17).

(Ƙ, ℓ) −span represents one of the applications of algebraic geometry in 3-dimensional projective space and to construct a complete (k, n) – arc in PG (3,17) where 3 ≤ n ≤ 307. We construct a complete (k, n) – arcs where n =3,4,5 , by selecting the union of some (k ,n) –arcs by using matlab19B program to find all complete ( k, n+1) – arc with the codes. We start with the points of index zero and the unit points, which we call the basic points of table ( 1 ). Then, we start adding points from the remaining points until we get intersections through which all points of the levels are deleted, then we repeat the process whenever we take different values for n. A (k, n) – arc. L corresponds to a projective [k, n, d]q-code of length k, dimension n, and we get distance d from the relation d = k – n and it achieves d ≤ k –n + 1. Moreover, we prove the complete (k ,n)-arc in PG(3,17).

The Viva committee was chaired by Prof. Dr. Amir Abdulillah Mohammed / University of Mosul, College of Education for Pure Science and the membership of Prof. Dr. Sinan Omer Ibrahim / University of Tikrit, College of Education for Girls, Asst. Prof. Zubaydah Muhammad Ibrahim/ University of Mosul, College of Computer Science and Mathematics and under the supervision and membership of Prof. Dr. Nada Yassen Kasm Yahya, University of Mosul, College of Education for Pure Science.