Möbius transforms, coincident Boolean functions and non-coincidence property of Boolean functions

Pieprzyk, Josef, Wang, Huaxiong, & Zhang, Xian-Mo (2011) Möbius transforms, coincident Boolean functions and non-coincidence property of Boolean functions. International Journal of Computer Mathematics, 88(7), pp. 1398-1416.

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Boolean functions and their Möbius transforms are involved in logical calculation, digital communications, coding theory and modern cryptography. So far, little is known about the relations of Boolean functions and their Möbius transforms. This work is composed of three parts. In the first part, we present relations between a Boolean function and its Möbius transform so as to convert the truth table/algebraic normal form (ANF) to the ANF/truth table of a function in different conditions. In the second part, we focus on the special case when a Boolean function is identical to its Möbius transform. We call such functions coincident. In the third part, we generalize the concept of coincident functions and indicate that any Boolean function has the coincidence property even it is not coincident.

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ID Code: 69351
Item Type: Journal Article
Refereed: Yes
Additional URLs:
Keywords: anti-coincident functions, Boolean functions, h-non-coincident functions, coincident functions, Non-coincident weight, Möbius transform
DOI: 10.1080/00207160.2010.509428
ISSN: 1029-0265
Divisions: Current > Schools > School of Electrical Engineering & Computer Science
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: © 2011 Taylor & Francis
Deposited On: 27 Mar 2014 03:34
Last Modified: 31 Mar 2014 01:30

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