The original paper "An Arithmetic Checksum for Serial Transmissions" is worthwhile reading. Fletcher's background as a physicist shows through and the analysis

The original paper "An Arithmetic Checksum for Serial Transmissions" is worthwhile reading. Fletcher's background as a physicist shows through and the analysis is interesting as it contrasts to many other papers I have read on codes. Also: note the section in the Wikipedia page on the Adler checksum, which was an attempt to improve Fletcher's checksum by substituting a prime modulus. This stands to reason as a prime modulus is usually important in codes. This change was probably not backed up by analysis and through direct simulation has shown to actually weaken the checksum. Just pointing this out as an example of what I have observed personally: people tinkering with codes (nothing wrong with that) to improve them, without bothering to understand the analysis they would have to do to prove that they hadn't made things actually worse. [yet another edit:] If you find error-detecting and -correcting codes interesting or mysterious, read the original papers! So many fun and interesting things to see there, and it is a chance to motivate a look into areas of math you might be unfamiliar with. 'Nuff said.