Title
Codes from Skew Polynomial Rings with Derivation
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics
Date of Award
Summer 2018
Abstract
In this paper, a special class of linear codes, named skew cyclic codes with derivation type is studied. These codes are constructed using a non-commutative ring called a skew polynomial ring of derivation type Fq[x;θ,δ], where Fq is a finite field of q elements. In this thesis, theory of error correcting codes is introduced at first and then skew codes of endomorphism and derivation type are considered. Algorithms for multiplication and division of polynomials in Fq[x;θ,δ]. are implemented. We use these algorithms to find factorizations of the polynomial x^n-1. These factorizations are used to construct codes over F4={ 0,1,w,w^2}. Finally, we provide examples using Magma-computational algebra system. Keywords: Skew codes, derivation, automorphism
Advisor
Padmapani Seneviratne
Subject Categories
Mathematics | Physical Sciences and Mathematics
Recommended Citation
Altin, Arife Dondu, "Codes from Skew Polynomial Rings with Derivation" (2018). Electronic Theses & Dissertations. 391.
https://digitalcommons.tamuc.edu/etd/391
