Graduation Year

2016

Date of Thesis Acceptance

Spring 5-11-2016

Major Department or Program

Mathematics

Advisor(s)

Patrick Keef

Abstract

The theory of error-correcting codes has historically been most useful in the context of linear codes. Such codes may be viewed as vector spaces over Galois fields carrying with them many familiar and well-studied properties. A generalization of Galois fields is the concept of Galois rings. It is therefore natural to consider codes over Galois rings to study which properties such codes maintain in the move to a more general setting. This thesis will present two separate expositions on coding theory and Galois rings. After this, the intersection of these topics will be considered: codes over Galois rings.

Page Count

56

Subject Headings

Error-correcting codes (Information theory), Coding theory -- Mathematics, Galois theory, Vector algebra, Whitman College 2016 -- Dissertation collection -- Mathematics Department

Permanent URL

http://hdl.handle.net/10349/201608091273

Document Type

Public Accessible Thesis

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Included in

Mathematics Commons

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