The Eigenfunction of the Reed-Muller Transformation
NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF ELECTRICAL AND COMPUTER ENGINEERING
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We introduce eigenfunctions of the Reed-Muller transform. Eigenfunctions are functions whose canonical sumof- products expression and PPRM positive polarity Reed- Muller expression are isomorphic. In the case of symmetric functions, the eigenfunction can be viewed as a function whose reduced truth vector is identical to the reduced Reed- Muller spectrum. We show that the number of symmetric ordinary eigenfunctions on n-variables is 2 n1 divided by 2 2 2n-1. We identify three special symmetric functions that correspond to the most complicated minimal fixed polarity Reed- Muller FPRM form. We show how the transeunt triangle can be used to convert between the reduced ordinary truth vector and the reduced ordinary Reed-Muller spectrum. We derive the number of products in the FPRM for these symmetric functions this shows that they have the most complicated minimal FPRM among all n-variable functions.
- Theoretical Mathematics