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2007 Counting Balanced Boolean Functions in $n$ Variables with Bounded Degree
Younhwan Cheon, Thomas W. Cusick
Experiment. Math. 16(1): 101-106 (2007).

Abstract

We consider the problem of obtaining good upper and lower bounds on the number of balanced Boolean functions in $n$ variables with degree less than or equal to $k$. This is the same as the problem of finding bounds on the number of codewords of weight $2^{n-1}$ in the Reed--Muller code of length $2^n$ and order $k$. We state several conjectures and use them to obtain good bounds. We believe that the conjectures will be highly useful for further research

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Younhwan Cheon. Thomas W. Cusick. "Counting Balanced Boolean Functions in $n$ Variables with Bounded Degree." Experiment. Math. 16 (1) 101 - 106, 2007.

Information

Published: 2007
First available in Project Euclid: 5 April 2007

zbMATH: 1219.94097
MathSciNet: MR2312980

Subjects:
Primary: 94C10
Secondary: 11T71 , 94B65

Keywords: balanced , Boolean functions , Reed-Muller codes

Rights: Copyright © 2007 A K Peters, Ltd.

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