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. 
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. 