Institut de Mathématiques de Luminy

Abstract 2006-11

Edoukou Frédéric.
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 XP3 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).

Keywords: arithmetical genus, functional codes, hermitian surface, hermitian curve, quadric, weight.


Last update : june 15, 2006, EL.