Open Access Senior Thesis
Bachelor of Science
2022 Benjamin R Langton
The recently proposed generalized covering radius is a fundamental property of error correcting codes. This quantity characterizes the trade off between time and space complexity of certain algorithms when a code is used in them. However, for the most part very little is known about the generalized covering radius. My thesis seeks to expand on this field in several ways. First, a new upper bound on this quantity is established and compared to previous bounds. Second, this bound is used to derive a new algorithm for finding codewords within the generalized covering radius of a given vector, and also to modify an existing algorithm, greatly improving its efficiency.
Langton, Benjamin, "Results on the Generalized Covering Radius of Error Correcting Codes" (2022). HMC Senior Theses. 265.