An
${\mathbb{F}}_{q}$linear
blocking set
$B$
of
$\pi =PG\left(2,{q}^{n}\right)$,
$q={p}^{h}$,
$n>2$,
can be obtained as the projection of a canonical subgeometry
$\Sigma \simeq PG\left(n,q\right)$ of
${\Sigma}^{\ast}=PG\left(n,{q}^{n}\right)$ to
$\pi $ from an
$\left(n3\right)$dimensional
subspace
$\Lambda $ of
${\Sigma}^{\ast}$, disjoint from
$\Sigma $, and in this case we
write
$B={B}_{\Lambda ,\Sigma}$. In this paper we
prove that two
${\mathbb{F}}_{q}$linear
blocking sets,
${B}_{\Lambda ,\Sigma}$
and
${B}_{{\Lambda}^{\prime},{\Sigma}^{\prime}}$, of
exponent
$h$
are isomorphic if and only if there exists a collineation
$\phi $ of
${\Sigma}^{\ast}$ mapping
$\Lambda $ to
${\Lambda}^{\prime}$ and
$\Sigma $ to
${\Sigma}^{\prime}$.
This result allows us to obtain a classification theorem for
${\mathbb{F}}_{q}$linear blocking
sets of the plane
$PG\left(2,{q}^{4}\right)$.
