scholarly journals Binary linear codes from vectorial boolean functions and their weight distribution

2017 ◽  
Vol 340 (12) ◽  
pp. 3055-3072 ◽  
Author(s):  
Deng Tang ◽  
Claude Carlet ◽  
Zhengchun Zhou
Keyword(s):  
Weight Distribution ◽  
Boolean Functions ◽  
Linear Codes ◽  
Binary Linear Codes ◽  
Vectorial Boolean Functions

Linear codes from vectorial Boolean functions in the context of algebraic attacks

2020 ◽  
pp. 2150032
Author(s):  
M. Boumezbeur ◽  
S. Mesnager ◽  
K. Guenda
Keyword(s):  
Boolean Functions ◽  
Linear Codes ◽  
Cyclic Codes ◽  
Weight Enumerator ◽  
Direct Link ◽  
Algebraic Attacks ◽  
Vectorial Boolean Functions ◽  
Lcd Codes ◽  
Vectorial Function ◽  
The Relationship

In this paper, we study the relationship between vectorial (Boolean) functions and cyclic codes in the context of algebraic attacks. We first derive a direct link between the annihilators of a vectorial function (in univariate form) and certain [Formula: see text]-ary cyclic codes (which we show that they are LCD codes). We also present some properties of those cyclic codes as well as their weight enumerator. In addition, we generalize the so-called algebraic complement and study its properties.

scholarly journals On the weight distribution of random binary linear codes

2019 ◽  
Vol 56 (1) ◽  
pp. 5-36 ◽  
Author(s):  
Nati Linial ◽  
Jonathan Mosheiff
Keyword(s):  
Weight Distribution ◽  
Linear Codes ◽  
Binary Linear Codes
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