Minimal Distances For Certain Quantum Product Codes And Tensor Products Of Chain Complexes (Vol 102, 062402, 2020)

We use a map to quantum error-correcting codes and a subspace projection to get lower bounds for minimal homological distances in a tensor product of two chain complexes of vector spaces over a finite field. Homology groups of such a complex are described by the Kunneth theorem. We give an explicit expression for the distances when one of the complexes is a linear map between two spaces. The codes in the construction, subsystem product codes and their gauge-fixed variants, generalize several known families of quantum error-correcting codes.