On the Balanced Elementary Symmetric Boolean Functions
Summary :
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E96-A No.2 pp.663-665
- Publication Date
- 2013/02/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E96.A.663
- Type of Manuscript
- LETTER
- Category
- Cryptography and Information Security
Authors
Keyword
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Longjiang QU, Qingping DAI, Chao LI, "On the Balanced Elementary Symmetric Boolean Functions" in IEICE TRANSACTIONS on Fundamentals,
vol. E96-A, no. 2, pp. 663-665, February 2013, doi: 10.1587/transfun.E96.A.663.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E96.A.663/_p
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@ARTICLE{e96-a_2_663,
author={Longjiang QU, Qingping DAI, Chao LI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Balanced Elementary Symmetric Boolean Functions},
year={2013},
volume={E96-A},
number={2},
pages={663-665},
abstract={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.},
keywords={},
doi={10.1587/transfun.E96.A.663},
ISSN={1745-1337},
month={February},}
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TY - JOUR
TI - On the Balanced Elementary Symmetric Boolean Functions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 663
EP - 665
AU - Longjiang QU
AU - Qingping DAI
AU - Chao LI
PY - 2013
DO - 10.1587/transfun.E96.A.663
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E96-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2013
AB - 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.
ER -
English
