Oh, and another limitation in that paper: to get positive zero-error rate, there has to be input symbols in the channel that cannot ever map to the same output channel, which is not the case for any binary channel in use I have ever seen (my PhD is in error correcting codes).

So if noise in the channel could turn a 0 to a 1, or a 1 to a 0, then there is never a positive zero-error rate.

This is explained in the paper, page 9, second column.

So this is an interesting math question for channels that don't occur in practice, and has resulted (as far as I can tell) in no working codes usable even in labs. It certainly does not apply to transmitting binary data over any noisy channels or media, which is where most if not all error correction codes are actually used.

The zero error capacity is defined for infinite length codes, none of which are usable in practice.

Another way to see it - care to list any error code used anywhere with zero error rate?

Read the paper. Shannon write about this in his 1956 paper and subsequent work analyses further, but it's theoretical, and probably not practical for any real world error codes.