Abstract

Finding best coset codes for secrecy over the binary erasure wiretap channel remains a difficult problem. Greater understanding of the structure of coset codes is necessary to reduce the problem space in which we search for these best codes. This dissertation presents new necessary conditions for a code to be best, including a condition that states that a code must maximize the minimum distance of both itself and its dual. It introduces and evaluates the accuracy of new heuristics to approximate the code's equivocation based on a code's weight enumerator polynomial. We also present a new tool for visualizing the structure of a code's generational graph. These insights allow us to create faster algorithms that we use to find best coset codes for secrecy. We present some of these algorithms with an analysis of their efficacy and speed.

Degree

PhD

College and Department

Ira A. Fulton College of Engineering; Electrical and Computer Engineering

Rights

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