# Linear approximattion of $(x+y) \bmod 2^n$ in FSM of SNOW 2.0 where $x,y$ in $F_{2}^n$

I would like to understand the linear approximation of $$(x+y) \bmod 2^n$$ by linear masking method in the paper refereed ""Improved Linear Distinguis'hers for SNOW 2.0" by Kaisa Nyberg and Johan Wall´en." In Page number 14 to 15, one theory has been given. I am unable to understand the $$A_r$$ matrix computation. Specially what is $$v$$ in this matrix. Advance thanks for anyone's kind explanation.

• please use mathjax and provide proper mathematical details – kodlu May 2 '20 at 23:47