On scatter properties of modular addition operation over imprimitivity systems of the translation group of the binary vector space

We study scatter properties of the modular addition operation for imprimitivity systems of the translation group of the binary vector space $V_n = \{0,1\}^n$. We describe all the subspaces of the space $V_n$ that induce imprimitivity systems with worst possible scatter by the modular addition operation.