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 <span style="font-family: Euclid Math Two">Z</span>ⁿ<sub style="margin-left:-6px;">2</sub> to arbitrary finite abelian groups, was able to show that if p &ge; 5 , then <span style="font-family: Euclid Math Two">Z</span>ⁿ<sub style="margin-left:-6px;">p</sub> 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.