On the balanced elementary symmetric Boolean functions
In this paper, we give some results towards the conjecture that σ2t+1l-1,2t are the only nonlinear balanced elementary symmetric Boolean functions where t and l are positive integers. At first, a unified and simple proof of some earlier results is shown. Then a property of balanced elementary symmet...
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sg-ntu-dr.10356-1001702023-02-28T19:37:10Z On the balanced elementary symmetric Boolean functions Qu, Longjiang Dai, Qingping Li, Chao School of Physical and Mathematical Sciences Mathematical Sciences In this paper, we give some results towards the conjecture that σ2t+1l-1,2t are the only nonlinear balanced elementary symmetric Boolean functions where t and l are positive integers. At first, a unified and simple proof of some earlier results is shown. Then a property of balanced elementary symmetric Boolean functions is presented. With this property, we prove that the conjecture is true for n=2m+2t-1 where m,t(m>t) are two non-negative integers, which verified the conjecture for a large infinite class of integer n. Published version 2014-01-13T02:20:50Z 2019-12-06T20:17:47Z 2014-01-13T02:20:50Z 2019-12-06T20:17:47Z 2013 2013 Journal Article Qu, L., Dai, Q., & Li, C. (2013). On the Balanced Elementary Symmetric Boolean Functions. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, E96.A(2), 663-665. https://hdl.handle.net/10356/100170 http://hdl.handle.net/10220/18451 10.1587/transfun.E96.A.663 en IEICE transactions on fundamentals of electronics, communications and computer sciences © 2013 The Institute of Electronics, Information and Communication Engineers. This paper was published in IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences and is made available as an electronic reprint (preprint) with permission of The Institute of Electronics, Information and Communication Engineers. The paper can be found at the following official DOI: [http://dx.doi.org/10.1587/transfun.E96.A.663]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. application/pdf |
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Mathematical Sciences Qu, Longjiang Dai, Qingping Li, Chao On the balanced elementary symmetric Boolean functions |
| description |
In this paper, we give some results towards the conjecture that σ2t+1l-1,2t are the only nonlinear balanced elementary symmetric Boolean functions where t and l are positive integers. At first, a unified and simple proof of some earlier results is shown. Then a property of balanced elementary symmetric Boolean functions is presented. With this property, we prove that the conjecture is true for n=2m+2t-1 where m,t(m>t) are two non-negative integers, which verified the conjecture for a large infinite class of integer n. |
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School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Qu, Longjiang Dai, Qingping Li, Chao |
| format |
Article |
| author |
Qu, Longjiang Dai, Qingping Li, Chao |
| author_sort |
Qu, Longjiang |
| title |
On the balanced elementary symmetric Boolean functions |
| title_short |
On the balanced elementary symmetric Boolean functions |
| title_full |
On the balanced elementary symmetric Boolean functions |
| title_fullStr |
On the balanced elementary symmetric Boolean functions |
| title_full_unstemmed |
On the balanced elementary symmetric Boolean functions |
| title_sort |
on the balanced elementary symmetric boolean functions |
| publishDate |
2014 |
| url |
https://hdl.handle.net/10356/100170 http://hdl.handle.net/10220/18451 |
| _version_ |
1759858364491235328 |