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]

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Just in case, here is also the questionable "theorem" from the 3rd (2013) edition of Erickson's book (thanks @spin for the pointer), which in the 2nd (1996) edition was numbered as *Theorem 9.3*.
Apparently, the statement about *"only two feasible sets of parameters for perfect codes"* is correct, but "theorem" as stated lacks a proof (and thus may be incorrect) and was not an argument for non-existence of other perfect codes. Reference [22] is Pless' book. [![Page 157 from Martin Erickson's "Introduction to Combinatorics" book (2013)][2]][2]


  [1]: https://i.sstatic.net/LCR20.png
  [2]: https://i.sstatic.net/gg1oc.png