9 June، 2022

Master Thesis Viva-Mathematics Department

Master Thesis Viva in the College of Education for Pure Science entitled “Applications of Hamming codes in 3-dimensional Projective Space of order seven”The College of Education for Pure Science, University of Mosul, has done the Master Thesis Viva entitled “Applications of Hamming codes in 3-dimensional Projective Space of order seven”,On Thursday, June 9, 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 Thakreen Faisal Sultan in the Department of Mathematics, The main objectives of this thesis are obtained by application of Hamming codes in 3- dimensional projective space and the application of Maximum distance separable and weight distribution (w .d) of optimal linear dimension (4D) in PG (3, 7), found the minimum distance d and determine type of linear code and apply the results to the 4D optimal linear code the inferred from cap. By (MATLAB) program, the thesis get new examples to the weight distribution of 4D optimal linear code

[n, k, d], code in PG (3, 7) , The new example are ( ((2.2.14),…,(2.2.1) ,also included is that the highest value of (k ,4)-cap is 148 according to this equation :constraint for (k,4)-cap in PG(t , q) for t=3 ,q=7 ,s=2Equation is : k ≤ (s ,q)- ( n+ s -2 ) …………(*)(s , q) =22Then maximal size of (k , 4)-cap in PG(t , q)= 148,and determine MDS codes of dimension four and erroe – correcting codes and hamming codes The goal is also to apply a certain theory to find out that MDS is Ham(r ,q) if it was d=3 and apply example on PG(3,q) ,(q=3,4,5,7), as well apply Hamming encoding on PG(3, q)(q=3,4,5,7). The Viva committee was chaired by Prof .Dr .Raida Dawood Mahmood from University of Mosul College Of Computer Science and Mathematics and the membership of Dr .chenar Abdul Kareem Ahmed from University of Zakho / College of Sciences, Dr. Ali Abdel Qader Bilal from University of Mosul College of Education For Pure Science and under the supervision and membership of Prof. Dr. Nada Yassen Kasm Yahya / Mosul University/College of Education for Pure Science.

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