تطبيقات جديدة لنظرية الترميز في الفضاء الإسقاطي PG(3,5)
New Applications of Coding Theory in PG(3,5)
- الباحث
- هاجر حيدر عبدالله
- المشرف
- ندى ياسين قاسم يحيى
- الجامعة
- جامعة الموصل
- الكلية / القسم
- كلية التربية للعلوم الصرفة / قسم الرياضيات
- الشهادة
- ماجستير
- السنة
- 2022
- لغة الرسالة
- انكليزي
- الكلمات المفتاحية
- Coding theory ; Projective space ; PG(3,5) ; Linear codes
Abstract
a This thesis 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 theo 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 . The new examples are :(2.1.16-2.1.25) 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=2 Then maximal size of (k, 4)-cap in PG(t, q)= 76 . The goal is also to apply a certain theorem 2.2.3 which states: A q- ary (n, M,2e +1)-code c satisfies M {( ) +( ) (q-1)+...+( ) } ...(**) and Corollary 2.2.4 which states: q- ary (n, M,2e +1)-code c is perfect if and only if equality holds in the equation(**). On 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 b 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. As we might call the special purpose of the work in the table (***) .
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