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If you ask a person to type in a page full of random hand written 20 digit numbers, I would expect that you would see different errors occur with non uniform frequency (e.g. switching 6 and 5 or 3 and 8 would be more common than 7 and 0). Are there any error correction codes that incorporate that sort of error functions into there construction?

The practical application of this is generating human enterable, error tolerant encodings for things like account numbers or cryptographic keys.