Error-correcting codes over Galois rings
Holdman, Gregory Reid
May 11, 2016
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.
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