Functional codes arising from quadric intersections with Hermitian varieties

We investigate the functional code Ch(X) introduced by G. Lachaud [10] in the special case where X is a non-singular Hermitian variety in PG(N, q2) and h = 2. In [4], F. Edoukou solved the conjecture of Sørensen [11] on the minimum distance of this code for a Hermitian variety X in PG(3, q2). In this paper, we will answer the question about the minimum distance in general dimension N , with N < O(q2). We also prove that the small weight codewords correspond to the intersection of X with the union of 2 hyperplanes.