  We present the second order contributions to the coefficient functions for
the parity violating polarized structure functions $g_L$ and $g_4$, thus
completing the $\mathcal{O}(\alpha_S^2)$ knowledge on DIS structure functions.
We obtain the missing $\mathcal{O}(\alpha_S^2)$ pieces from the known parity
conserving unpolarized coefficient functions. We also present a
phenomenological analysis for the phase space region the future Electron-Ion
Collider is set to explore.
