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Cyclic Codes and Cyclic Lattices

In this thesis, we review basic properties of linear codes and lattices with a certain focus on their interplay. In particular, we focus on the analogous con- structions of cyclic codes and cyclic lattices. We start out with a brief overview of the basic theory and properties of linear codes. We then demonstrate the construction of cyclic codes and emphasize their importance in error-correcting coding theory. Next we survey properties of lattices, focusing on algorithmic lattice problems, exhibit the construction of cyclic lattices and discuss their applications in cryptography. We emphasize the similarity and common prop- erties of the two cyclic constructions.

Identiferoai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:cmc_theses-2772
Date01 January 2017
CreatorsMaislin, Scott
PublisherScholarship @ Claremont
Source SetsClaremont Colleges
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceCMC Senior Theses
Rights© 2017 Scott E Maislin, http://creativecommons.org/licenses/by/4.0/

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