The Construction and Enumeration of Symmetric Balanced Boolean Functions

doi:10.13190/jbupt.200605.15.162

JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM ›› 2006, Vol. 29 ›› Issue (5): 15-18.doi: 10.13190/jbupt.200605.15.162

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The Construction and Enumeration of Symmetric Balanced Boolean Functions

MO Jiao , WEN Qiao-yan

School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

Received:2005-01-01 Revised:1900-01-01 Online:2006-10-30 Published:2006-10-30
Contact: MO Jiao

Abstract

Abstract:

It is known in conference [1] that the construction and enumeration of symmetric balanced Boolean functions is equivalent to the solution of the knapsack equation and enumeration of the solutions. In this paper, we first find out a set of solutions of this equation when is odd and the number of the elements in is given, then we obtain the necessary and sufficient condition under which there exists other solutions of the equation out of the set .We also show a method for finding out the solutions out of the set . At last some solutions of the equation is given when .

Key words: balanced functions, symmetric functions, strict avalanche criterion, knapsack equation

CLC Number:

TN918.1

MO Jiao , WEN Qiao-yan. The Construction and Enumeration of Symmetric Balanced Boolean Functions[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2006, 29(5): 15-18.

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The Construction and Enumeration of Symmetric Balanced Boolean Functions

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