CONICET | Buscador de Institutos y Recursos Humanos

Given a suitable extension $F´/F$ of algebraic function fields over a finite field $F_q$, we introduce the conorm code $Con_{F´/F}(C)$ defined over $F´$ which is constructed from an algebraic geometry code $C$ defined over $F$. We study the parameters of $Con_{F´/F}(C)$ in terms of the parameters of $C$, the ramification behavior of the places used to define $C$ and the genus of $F$.In the case of unramified extensions of function fields we prove that $Con_{F´/F}(C)^perp = Con_{F´/F}(C^perp)$ when the degree of the extension is coprime to the characteristic of $F_q$. 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.