I've encountered a system where I need to construct a sort of quasi block code:
We want to encode a symbol $s$ from a finite-sized alphabet $\mathcal{S}$ using $N$ segments of information. The $i^{th}$ segment must come from the alphabet $A_i$.
We are tasked with designing a code for this encoder. The code will be a 1-1 function: $$C:\mathcal{S}\rightarrow A_1\times A_2 \times \dots \times A_N$$
What is the code with the highest possible minimum hamming distance between elements in its range?
Note that this is not the same as a "variable-length block code."
Note that if $|S|=2^m,$ and $\underset{i}{\max} |A_i|=2^n$ we could just examine binary (m,n) block codes, and take the best one that varies little enough that it can be re-written as a function onto $A_1 \times \dots \times A_N$.