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

Here is the questionable "theorem" from the 2nd (2013) edition of Erickson's book (thanks @spin for the pointer), which in the 1st (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)][1]][1]

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And here are two pages (pages 23-24) with a relevant discussion from the 3rd (1998) edition of Pless' book. It does mention Tietäväinen and van Lint results on page 24, but they do not imply the "theorem" from Erickson's book. Reference [29] is 

> A. Tietäväinen, ["On the nonexistence of perfect codes over finite
> fields"](https://epubs.siam.org/doi/pdf/10.1137/0124010), *SIAM J.
> Appl. Math.* 24 (1973), 88-96.

[![Page 23 from Vera Pless "Introduction to the Theory of Error-correcting Codes" book (1998)][2]][2]
[![Page 24 from Vera Pless "Introduction to the Theory of Error-correcting Codes" book (1998)][3]][3]

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