نتائج جديدة لبناء الشفرات الناشئة من الامتداد (k,ℓ) في PG(3,17)
New Results for Construction Codes Arised from (k,ℓ)-span in PG(3,17)
- الباحث
- دخيل عبدالقادر الياس
- المشرف
- ندى ياسين قاسم يحيى
- الجامعة
- جامعة الموصل
- الكلية / القسم
- كلية التربية للعلوم الصرفة / قسم الرياضيات
- الشهادة
- ماجستير
- السنة
- 2023
- لغة الرسالة
- انكليزي
- الكلمات المفتاحية
- Linear Codes ; (k,ℓ)-span ; Projective Space PG(3,17) ; Coding Theory
Abstract
A The Purpose of this thesis is to construct codes arising from complete (k,l) – span in PG (3,17) and find new code arising from complete (k,n) - arcs in PG (3, 17) over Galois fields . Which represents one of applications of algebraic geometry. We get the following results first, we found the points, lines and planes in PG (3,17) and we construct (k,l) − span which is a set of k lines no two of which intersect when k = q2 +1- nq , q = 17, 0 ≤ n ≤ 2 q +1, n =10 we also found alinear code [k,n,d] - code of length k and dimension n satiesfies d = k - n+1. Second, construct a complete (k, n) – arc in PG (3,17) where 3 ≤ n ≤ 307 (we explain that n between {3,307} n= 3 three dimension ,n =q2 +q +1,q = 17) 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(The remaining points are the points that appear after deleting the lines on which the triple and quadruple intersections are located, etc. from the required intersections( 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 corresponds to a projective [k, n, d] - code .
طلب نسخة من الملف
الملفات غير منشورة على الموقع. اترك بياناتك وسيتواصل معك موظفو قسم الشؤون الثقافية والفنون لإرسال النسخة مجاناً.