Calderbank, RobertWang, Weiyao2018-04-252018-04-252018-04-25https://hdl.handle.net/10161/16531This 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.en-USWeyl TransformReed-Muller CodeQuantum Error-CorrectionCoding TheoryHeisenberg-Weyl GroupSymplectic GeometryHonors thesis