Sarah Spence
Sarah Spence

Ph.D. (2002) Cornell University

First Position
Dissertation
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Abstract: This dissertation considers codes that are formed using certain subsets of algebraic errorcontrol codes and signal space codes. We first consider subspace subcodes of ReedSolomon (SSRS) codes. We prove a conjecture of Hattori concerning how to identify subspaces that give an SSRS code whose dimension exceeds a certain lower bound.
We next consider generalized coset codes, which are built using partitions of signal space codes. We extend the concepts of generalized coset codes in Euclidean space by defining generalized coset codes in Lee space. We prove that all linear codes over Z_m are realizable as these new Leegeneralized coset codes. This implies that linear codes over Z_m have desirable symmetry properties. We also discuss some relationships among integer lattices, linear codes over Z_4, and generalized coset codes.