In the traditional two-rack distributed storage system (DSS) model, due to the assumption that the storage capacity of each node is the same, the minimum bandwidth regenerating (MBR) point becomes infeasible. In this paper, we design a new non-homogeneous two-rack model by proposing a generalization of the threshold function used to compute the tradeoff curve. We prove that by having the nodes in the rack with higher regenerating bandwidth stores more information, all the points on the tradeoff curve, including the MBR point, become feasible. Finally, we show how the non-homogeneous two-rack model outperforms the traditional model in the tradeoff curve between the storage per node and the repair bandwidth.

Recently, new families of quaternary linear Reed–Muller codes have been introduced. They satisfy that, after the Gray map, the corresponding${\BBZ}_{4}$-linear codes have the same parameters and properties as the codes of the binary linear Reed–Muller family. A structural invariant, the dimension of the kernel, for binary codes is used to classify completely these${\BBZ}_{4}$-linear codes. The dimension of the kernel for these${\BBZ}_{4}$-linear codes is established generalizing the known results about the dimension of the kernel for${\BBZ}_{4}$-linear Hadamard and${\BBZ}_{4}$-linear extended 1-perfect codes.