  Given a suitable extension $F'/F$ of algebraic function fields over a finite
field $\mathbb{F}_q$, we introduce the conorm code
$\text{Con}_{F'/F}(\mathcal{C})$ defined over $F'$ which is constructed from an
algebraic geometry code $\mathcal{C}$ defined over $F$. We study the parameters
of $\text{Con}_{F'/F}(\mathcal{C})$ in terms of the parameters of
$\mathcal{C}$, the ramification behavior of the places used to define
$\mathcal{C}$ and the genus of $F$. In the case of unramified extensions of
function fields we prove that $\text{Con}_{F'/F}(\mathcal{C})^\perp =
\text{Con}_{F'/F}({\mathcal{C}}^\perp)$ when the degree of the extension is
coprime to the characteristic of $\mathbb{F}_q$. We also study the conorm of
cyclic algebraic-geometry codes and we show that some repetition codes,
Hermitian codes and all Reed-Solomon codes can be represented as conorm codes.
