  Let $\mathbb{F}_{q}$ be a finite field with $q$ elements, where $q$ is a
power of prime $p$. A polynomial over $\mathbb{F}_{q}$ is square-free if all
its monomials are square-free. In this note, we determine an upper bound on the
number of zeroes in the affine torus $T=(\mathbb{F}_{q}^{*})^{s}$ of any set of
$r$ linearly independent square-free polynomials over $\mathbb{F}_{q}$ in $s$
variables, under certain conditions on $r$, $s$ and degree of these
polynomials. Applying the results, we partly obtain the generalized Hamming
weights of toric codes over hypersimplices and square-free evaluation codes, as
defined in \cite{hyper}. Finally, we obtain the dual of these toric codes with
respect to the Euclidean scalar product.
