Guangqi

In the case of higher dimensional hypergraph product codes, the logical operators of these codes have the structure analogous to classical tensor product code. Although it's not formal, I think it provides a way for analyzing the distance. I'm also writing about this currently.

In classical coding theory, for two linear codes with parameters $[n_1, k_1, d_1]$ and $[n_2, k_2, d_2]$, it seems well know that their tensor product code has the parameters $[n_1n_2, k_1k_2, d_1d_2]$. (See definition 6 of www.cs.purdue.edu/homes/pvalia...)

Is this what you are looking for? arxiv.org/pdf/1810.01519