2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119887We study the functional codes $C_h(X)$ defined by G. Lachaud in $\lbrack 10 \rbrack$ where $X \subset {\mathbb{P}}^N$ is an algebraic projective variety of degree $d$ and dimension $m$. When $X$ is a hermitian surface in $PG(3,q)$, Sørensen in \lbrack 15\rbrack, has conjectured for $h\le t$ (where $q=t^2$) the following result : $$# X_{Z(f)}(\mathbb{F}_{q}) \le h(t^{3}+ t^{2}-t)+t+1$$ which should give the exact value of the minimum distance of the functional code $C_h(X)$. In this paper we resolve the conjecture of Sørensen in the case of quadrics (i.e. $h=2$), we show the geometrical structure of the minimum weight codewords and their number; we also estimate the second weight and the geometrical structure of the codewords reaching this second weightaccepted for publication in Finite Fields and Their ApplicationsAlgebraic Geometry05B25, 11T71, 14J29text