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In this paper, several new classes of Boolean functions with few Walsh transform values, including bent, semi-bent and five-valued functions, are obtained by adding the product of two or three linear functions to some known bent functions.Numerical results show that the proposed class contains cubic bent functions that are affinely inequivalent to all known quadratic ones. Meanwhile, we determine the distribution of the Walsh spectrum of five-valued functions constructed in this paper.

Details

1009240
Subject
Boolean functions;
Boolean algebra;
Walsh transforms;
Linear functions
Identifier / keyword
Information Theory; Combinatorics; Information Theory
URL
http://arxiv.org/abs/1506.04886
Title
Several new classes of Boolean functions with few Walsh transform values
Author
Xu, Guangkui; Cao, Xiwang; Xu, Shanding
Publication title
arXiv.org; Ithaca
Publication year
2015
Publication date
Jun 16, 2015
Section
Computer Science; Mathematics
Publisher
Cornell University Library, arXiv.org
Source
arXiv.org
Place of publication
Ithaca
Country of publication
United States
University/institution
Cornell University Library arXiv.org
Publication subject
Biology, Statistics, Physics, Mathematics, Engineering--Electrical Engineering, Computers--Computer Engineering, Business And Economics--Banking And Finance
e-ISSN
2331-8422
Source type
Working Paper
Language of publication
English
Document type
Working Paper
Publication history
 
 
Online publication date
2015-06-17
Milestone dates
2015-06-16 (Submission v1)
Publication history
 
 
   First posting date
17 Jun 2015
ProQuest document ID
2082682017
Document URL
https://www.proquest.com/working-papers/several-new-classes-boolean-functions-with-few/docview/2082682017/se-2?accountid=208611
Full text outside of ProQuest
http://arxiv.org/abs/1506.04886
Copyright
© 2015. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Last updated
2019-04-13
Database
ProQuest One Academic