On the distribution of auto-correlation value of balanced Boolean functions | Zendy

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On the distribution of auto-correlation value of balanced Boolean functions

Author(s) -

Yu Zhou

Publication year - 2013

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2013.7.335

Subject(s) - mathematics , boolean function , upper and lower bounds , combinatorics , distribution (mathematics) , discrete mathematics , class (philosophy) , parity function , set (abstract data type) , boolean network , canonical normal form , correlation , boolean expression , value (mathematics) , statistics , algorithm , mathematical analysis , artificial intelligence , computer science , programming language , geometry

In this paper, we study the lower bound on the sum-of-square indicator of balanced Boolean functions obtained by Son, et al. in 1998, and give a sufficient and necessary condition under which balanced Boolean functions achieve this lower bound. We introduce a new general class of balanced Boolean functions in n variables (n ≥ 4) with optimal auto-correlation dis-tribution, and we study two sub-classes more explicitely. Finally, we study the sets of Boolean functions having a same auto-correlation distribution, and derive a lower bound on the number of elements in such set. © 2013 AIMS.

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