Let
q=
pe
\mathbb Fq{\mathbb F}_q
. Denote by
\mathbb Fq{\mathbb F}_q
. In this paper the full automorphism group of
(q) is determined affirming the conjecture of Brouwer [Des. Codes Cryptograph. 21, 69–76 (2000)]. The proof combines spectral and Schur ring techniques.