Extend the MHC construction to Galois qudits

Extend the qudit many-hypercube code construction from prime-dimensional qudits with arithmetic over $F_q\cong Z_q$ to Galois qudits of dimensions $q=p^r$ with $r>1$.

Background

The construction in the paper is restricted to prime dimensions, for which the finite field $F_q$ is isomorphic to $Z_q$. For prime-power dimensions with exponent $r>1$, this isomorphism does not hold, and the paper notes that a Galois-qudit formulation is more appropriate. Developing the corresponding code and operator construction for these dimensions remains unresolved.