New Quantum Codes from CSS Codes

We present a new propagation rule for CSS codes. Starting with a CSS code $[\text{\hspace{0.17em}⁣}[n,k,d]\text{\hspace{0.17em}⁣}{]}_q$, we construct a CSS code with parameters $[\text{\hspace{0.17em}⁣}[n-2,k,d-1]\text{\hspace{0.17em}⁣}{]}_q$. In general, one would only obtain a code with parameters $[\text{\hspace{0.17em}⁣}[n-2,k,d-2]\text{\hspace{0.17em}⁣}{]}_q$. The construction applies to asymmetric quantum codes from the CSS construction as well.