On tensor products of CSS Codes

Understand

CSS codes are in one-to-one correspondance with length 3 chain complexes.

• The latter are naturally endowed with a tensor product $\otimes$ which induces a similar operation on the former.
• We investigate this operation, and in particular its behavior with regard to minimum distances.
• Given a CSS code $\mathcal{C}$, we give a criterion which provides a lower bound on the minimum distance of $\mathcal{C} \otimes \mathcal{D}$ for every CSS code $\mathcal D$.