Writing $L_{i[j}L^{q}_{k]}$ with $\Gamma$ and $g_{ij}$

Question

Write $$L_{i[j}L^{q}_{k]}$$ with $\Gamma$ and $g_{ij}$

How should I start? I know that $$L_{i[j}L^{q}_{k]}$$ is called skew-symmetrisation notation is it

$$L_{i[j}L^{q}_{k]}=L_{ij}L^{q}_{k}-L_{ik}L^{q}_{j}$$?