Heaps for error correction and the geometry of non-linear loop-transversal codes

Abstract

This thesis builds on the paper Linear and Nonlinear Loop-Transversal Codes in Error Correction and Graph Domination of Dagli et al. The goal is to establish a more general framework for error correcting codes and the loop-transversal code construction. We examine the specific example studied by Dagli et al. within this more general framework, with specific interest in the geometry of the structure. The intention of the work is to open the door to a deeper understanding of the connections between these loop-transversal codes and the coding scheme as a whole.