Hello,
I would like to know if the theory of linear equalities and non-equalities exists in this sense :
You have $n-$bits strings $P_1, ..., P_{2k+1}, \lambda_1, ..., \lambda_k$ and we consider the addition in $(\mathbb{Z}/2\mathbb{Z})^n$.
What is the minimum number of solution (or at least a good approximation) of the following system :
$$P_{2i}\oplus P_{2i+1}=\lambda_i, \forall i\leq k$$
$$\forall i,j, \qquad i\neq j\implies P_i\neq P_j$$
