Additive bases of vector spaces over prime fields

Abstract

It is shown that for any t > cplog n linear bases B1, ..., Bt of Zpn their union (with repetitions) ∪i = 1t Bi forms an additive basis of Zpn; i.e., for any x ε{lunate} Zpn there exist A1 ⊃ B1, ..., At ⊃ Bt such that x = Σi = 1t Σy ε{lunate} Ai y. © 1991.