This is a follow-up to John's answer. 

Just for the record, this is the page with a relevant discussion from Pless' book. It does not have any "theorem", let alone a proof, that Erickson attributes to it. [![Page 23 from Vera Pless "Introduction to the Theory of Error-correcting Codes" book][1]][1]


  [1]: https://i.sstatic.net/LCR20.png