Codes from Skew Polynomial Rings with Derivation

Author

Arife Dondu Altin

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