Ju l 2 02 0 Künneth theorem with a distance

We use a map to certain quantum error-correcting codes to get a lower bound for minimal homological distances in a tensor product of two chain complexes of vector spaces over a finite field. This gives 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, give a generalization of several known families of quantum error-correcting codes.