Understanding Operator Reed-Muller Codes Through the Weyl Transform
| dc.contributor.advisor | Calderbank, Robert | |
| dc.contributor.author | Wang, Weiyao | |
| dc.date.accessioned | 2018-04-25T16:39:50Z | |
| dc.date.available | 2018-04-25T16:39:50Z | |
| dc.date.issued | 2018-04-25 | |
| dc.department | Mathematics | |
| dc.description.abstract | This paper expands the framework on the multidimensional generalizations of binary Reed-Muller code, operator Reed-Muller codes, where the codewords are projection operators through the Weyl Transform. The Weyl Transform of these operator Reed- Muller codes maps the operators to vectors, and it is isometric. This nice property gives new proofs for some known results and produce a simpler decoding algorithm. In particular, the property provides a different framework to analyze the distance spectrum of second operator Reed-Muller codes without using the Dickson’s Theorem. | |
| dc.identifier.uri | ||
| dc.language.iso | en_US | |
| dc.subject | Weyl Transform | |
| dc.subject | Reed-Muller Code | |
| dc.subject | Quantum Error-Correction | |
| dc.subject | Coding Theory | |
| dc.subject | Heisenberg-Weyl Group | |
| dc.subject | Symplectic Geometry | |
| dc.title | Understanding Operator Reed-Muller Codes Through the Weyl Transform | |
| dc.type | Honors thesis | |
| duke.embargo.months | 0 |