  A geometrically local quantum code is an error correcting code situated
within $\mathbb{R}^D$, where the checks only act on qubits within a fixed
spatial distance. The main question is: What is the optimal dimension and
distance for a geometrically local code? Recently, Portnoy made a significant
breakthrough with codes achieving optimal dimension and distance up to
polylogs. However, the construction invokes a somewhat advanced mathematical
result that involves lifting a chain complex to a manifold. This paper bypasses
this step and streamlines the construction by noticing that a family of good
quantum low-density parity-check codes, balanced product codes, naturally
carries a two-dimensional structure. Together with a new embedding result that
will be shown elsewhere, this quantum code achieves the optimal dimension and
distance in all dimensions. In addition, we show that the code has an optimal
energy barrier. We also discuss similar results for classical codes.
