Hermitian Duality and Syndrome Structure of CSS-Type Codes over the ring $\mathbb{Z}_q[i]$

We study the algebraic structure of principal ideal codes and CSS-type stabilizer constructions over the ring $ R_q=\mathbb Z_q[i],$ where every prime divisor of $q$ is congruent to $1$ modulo $4$. Although such ring-based constructions have recently been considered in the context of classical and q