Higher-Dimensional Quantum Hypergraph-Product Codes with Finite Rates

We describe a family of quantum error-correcting codes which generalize both the quantum hypergraph-product codes by Tillich and Zémor and all families of toric codes on $m$-dimensional hypercubic lattices. Parameters of the constructed codes, including the minimum distances, are given explicitly in terms of those of binary codes associated with the matrices used in the construction.