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Document Details
Document Type
:
Thesis
Document Title
:
Structure of Self-orthogonal Codes over Non-unital Rings
بناء الترميزات ذاتية التعامد على الحلقات الغير أحادية
Subject
:
Faculty of Science
Document Language
:
Arabic
Abstract
:
There are particular local rings E and I of order 4; without multiplicative identity, E (non-commutative) and I (commutative) defined by E=
I=
We study the algebraic structure of linear codes over these rings, in particular their residue and torsion codes. We introduce the notion of quasi self-dual codes over E and I, and Type IV codes, that is quasi self-dual codes all codewords of which have even Hamming weight. We study the weight enumerators of these codes over E by means of invariant theory, and classify them for short lengths. Further, for the ring I we defined quasi Type IV codes to be QSD codes with an even torsion code. We give a mass formula for QSD codes, and for quasi Type IV codes, and classify both of these also for short lengths.
Supervisor
:
Prof. Adel Nayef Al-Ahmadi
Thesis Type
:
Doctorate Thesis
Publishing Year
:
1442 AH
2020 AD
Added Date
:
Sunday, March 14, 2021
Researchers
Researcher Name (Arabic)
Researcher Name (English)
Researcher Type
Dr Grade
Email
وديان حسن باصفار
Basaffar, Widyan Hassan
Researcher
Doctorate
Files
File Name
Type
Description
46957.pdf
pdf
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