Table of Contents
Journal of Discrete Mathematics
Volume 2013 (2013), Article ID 270424, 12 pages
http://dx.doi.org/10.1155/2013/270424
Research Article

Classification of Boolean Functions Where Affine Functions Are Uniformly Distributed

1Applied Statistics Unit, Indian Statistical Institute, Kolkata 700108, India
2Institute of Mathematics and Applications, Bhubaneswar 751003, India

Received 17 May 2013; Revised 22 August 2013; Accepted 11 September 2013

Academic Editor: Pantelimon Stǎnicǎ

Copyright © 2013 Ranjeet Kumar Rout et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The present paper on classification of -variable Boolean functions highlights the process of classification in a coherent way such that each class contains a single affine Boolean function. Two unique and different methods have been devised for this classification. The first one is a recursive procedure that uses the Cartesian product of sets starting from the set of one variable Boolean functions. In the second method, the classification is done by changing some predefined bit positions with respect to the affine function belonging to that class. The bit positions which are changing also provide us information concerning the size and symmetry properties of the classes/subclasses in such a way that the members of classes/subclasses satisfy certain similar properties.