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

Here is 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.

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", SIAM J. Appl. Math. 24 (1973), 88-96.

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.

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", SIAM J. Appl. Math. 24 (1973), 88-96.

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.

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

Here is 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.

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", SIAM J. Appl. Math. 24 (1973), 88-96.

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 Erickson's book. Apparently, the statement about "only two feasible sets of parameters for perfect codes" is correct, but Theorem 9.3 as stated is not proved.

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.