> If that error is uniformly random, then a 128-bit sum is optimal and no different than 128-bit hash.
If the data you read is uniformly random then what you say is correct. But if there is a single error (bit/byte/word whatever) which is placed uniformly randomly and takes a uniformly random value then other codes are vastly stronger than using a hash.
While what you say is technically correct-- that a 'uniformly random error' means replacing the input with an entirely independent input, that isn't what most people would call an 'error' and isn't the kind of error that most applications of a check value would detect.
If the data you read is uniformly random then what you say is correct. But if there is a single error (bit/byte/word whatever) which is placed uniformly randomly and takes a uniformly random value then other codes are vastly stronger than using a hash.
While what you say is technically correct-- that a 'uniformly random error' means replacing the input with an entirely independent input, that isn't what most people would call an 'error' and isn't the kind of error that most applications of a check value would detect.