The Notes on the Linear Structures of Rotation Symmetric Boolean Functions

2013 ◽  
Vol 34 (9) ◽  
pp. 2273-2276 ◽  
Author(s):  
Guang-pu Gao ◽  
Wen-fen Liu
Keyword(s):  
Boolean Functions ◽  
Linear Structures ◽  
Symmetric Boolean Functions ◽  
Rotation Symmetric ◽  
Rotation Symmetric Boolean Functions

On the Conjecture About the Linear Structures of Rotation Symmetric Boolean Functions

2017 ◽  
Vol 28 (07) ◽  
pp. 819-833
Author(s):  
Lei Sun ◽  
Fangwei Fu ◽  
Jian Liu
Keyword(s):  
Normal Form ◽  
Boolean Functions ◽  
Homogeneous Component ◽  
Linear Structures ◽  
Symmetric Boolean Functions ◽  
Variable Formula ◽  
Rotation Symmetric ◽  
Algebraic Normal Form ◽  
Rotation Symmetric Boolean Functions

In this paper, we study the conjecture that [Formula: see text]-variable ([Formula: see text] odd) rotation symmetric Boolean functions with degree [Formula: see text] have no non-zero linear structures. We show that if this class of RSBFs have non-zero linear structures, then the linear structures are invariant linear structures and the homogeneous component of degree [Formula: see text] in the function’s algebraic normal form has only two possibilities. Moreover, it is checked that the conjecture is true for [Formula: see text], and then a more explicit conjecture is proposed.

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