Understanding Operator Reed-Muller Codes Through the Weyl Transform

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2018-04-25

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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.

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Wang, Weiyao (2018). Understanding Operator Reed-Muller Codes Through the Weyl Transform. Honors thesis, Duke University. Retrieved from https://hdl.handle.net/10161/16531.


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