Code Properties of the Holographic Sierpinski Triangle

We study the holographic quantum error correcting code properties of a Sierpinski Triangle-shaped boundary subregion in $Ad{S}_4\mathrm{/}CF{T}_3$. Due to existing no-go theorems in topological quantum error correction regarding fractal noise, this gives holographic codes a specific advantage over topological codes. We then further argue that a boundary subregion in the shape of the Sierpinski gasket in $Ad{S}_5\mathrm{/}CF{T}_4$ does not possess these holographic quantum error correction properties.