That is, however, error detection and not error correction.

Once an error is detected you can apply 'correction' to the nearest probably correct value .. which only 'works' for errors under a threshold.

Hence the assertion in comment above yours.

A 32 bytes hash for every 32 bytes? Then you double your storage requirements.

There are actually WAY better algorithms for this than a hash (a hash is meant to handle secrets and cryptography - it's the wrong thing for this purpose).

ECC codes can tell you if the data is bad - and you can choose how many bytes this covers, and that can also fix bad data, again, you can choose how many errors per byte you want.

If you are curious: https://en.wikipedia.org/wiki/Error_correction_code

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.

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.