College of Education for Pure Science

Master Thesis Viva in the College of Education for Pure Science entitled “New Applications of coding theory in 3-dimensional projective space of order five”The College of Education for Pure Science, University of Mosul, has done the Master Thesis Viva entitled “New Applications of coding theory in 3-dimensional projective space of order five “,On Wednesday, June 8, 2022, 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 M.Sc. student Hajir Hayder Abdullah Muhammad in the Department of Mathematics, includes objectives concerned with expanding the general concept of the projective plane and projective space, and theories and definitions that intervene in each item of this thesis. Through which we obtain certain results in this aspect.as well as the goal of it embodied in another dimension, which is to provide new examples of the distribution of weights and how to distribute weights for the optimal linear code. through a theory that we applied to each of the examples of PG(3,5) and we obtained the weights by entering certain values.They are related to certain matrices in the Matlab program and also included higher values ​​based on a fixed equation an is the equation .(*) The information and the equation indicate that the highest value of (k,4)-cap is 76.Equation is: k ≤ (s, q) – q( n+ s -2 ) …………(*)(s, q) =16 ,in PG(t, q) t=3,q=5,s=2Then maximal size of (k, 4)-cap in PG(t, q)= 76The goal is also to apply a certain theory which states:A q- ary (n, M,2e +1)-code c satisfiesM {+(q-1)+………………+}and Corollary which states: q- ary (n, M,2e +1)-code c is perfect if and only if equality holds in the above equationOn PG (3, 5)as the theory in other sources was on smaller fields, example ( field 3 in the projective plane and field 4 in the projective plane ) that is, it was expanded in space, and we obtained values ​​for the smallest distance, we benefited from it in applying a result that shows us perfect cases as in this code.C is a(31,,6)-code, and finally the goal is also to apply that theory to field 5 in space and field 3 and 2.Through these values, we show the difference between the same fields in space and plane and we benefited from them by finding the difference between the least distance, as it was not the same value despite the similarity of the fields. The table (3.3.6) shows us the difference. The Viva committee was chaired by Prof. Dr. Ammar Saddiq Mahmood the Head of Mathematics Department and the membership of Dr .chenar Abdul Kareem Ahmed from University of Zakho / College of Sciences, Ass. Prof. Zubaydah Muhammad Ibrahim from University of Mosul /College of Computer Sciences and Mathematics and under the supervision and membership of Prof. Dr. Nada Yassen Kasm Yahya / Mosul University/College of Education for Pure Science.