de Mathématiques de Luminy
The weight distribution of the functional codes defined by forms of degree 2 on hermitian surfaces
We study the functional codes C2(X) defined on a pro jective variety X , in the case where X ⊂ P3 is a non-degenerate hermitian surface. We first give some bounds for, which are better than the ones known. We compute the number of codewords reaching the second weight. We also estimate the third weight, show the geometrical structure of the codewords reaching this third weight and compute their number. The paper ends with a conjecture on the fourth weight and the fifth weight of the code C2(X).