On some batch code properties of the simplex code

The binary k -dimensional simplex code is known to be a 2 k - 1 -batch code and is conjectured to be a 2 k - 1 -functional batch code. Here, we offer a simple, constructive proof of a result that is “in between” these two properties. Our approach is to relate these properties to certain (old and new) additive problems in finite abelian groups. We also formulate a conjecture for finite abelian groups that generalizes the above-mentioned conjecture.