Non-Full Rank Factorization of Finite Abelian Groups

Abstract

Tilings of p-groups are closely associated with error-correcting codes. In [1], M. Dinitz, attempting to generalize full-rank tilings of  Zn2  to arbitrary finite abelian groups, was able to show that if p ≥5, then Znp  admits full-rank tiling and left the case p=3, as an open question. The result proved in this paper the settles of the question for the case p=3.