Open Access. Powered by Scholars. Published by Universities.®
- Institution
- Keyword
Articles 1 - 2 of 2
Full-Text Articles in Theory and Algorithms
Decoding Cyclic Codes Via Gröbner Bases, Eduardo Sosa
Decoding Cyclic Codes Via Gröbner Bases, Eduardo Sosa
Honors Theses
In this paper, we analyze the decoding of cyclic codes. First, we introduce linear and cyclic codes, standard decoding processes, and some standard theorems in coding theory. Then, we will introduce Gr¨obner Bases, and describe their connection to the decoding of cyclic codes. Finally, we go in-depth into how we decode cyclic codes using the key equation, and how a breakthrough by A. Brinton Cooper on decoding BCH codes using Gr¨obner Bases gave rise to the search for a polynomial-time algorithm that could someday decode any cyclic code. We discuss the different approaches taken toward developing such an algorithm and …
Surface Reconstruction Library, Jhye Tim Chi
Surface Reconstruction Library, Jhye Tim Chi
Honors Theses
The project aims to convert an arbitrary point cloud into a triangular mesh. Point clouds are a list of 3d points that model the topology of an object. Point clouds can have various issues, such as missing or noisy data. For the scope, we had no control over point cloud generation. We were also unable to deal with underlying registration or alignment problems. Triangular meshes are a list of triangles that have 3d vertices. This aggregate list of triangles defines the reconstructed surface. Our project implementation is based on Alexander Hornung and Leif Kobbelt’s method for surface reconstruction using the …