The weight distribution of the functional codes defined by forms of degree 2 on hermitian surfaces

Details The weight distribution of the functional codes defined by forms of degree 2 on hermitian surfaces The weight distribution of the functional codes defined by forms of degree 2 on hermitian surfaces

2005-12-20

arxiv.org/abs/math/0512476v1

Mathematics

Algebraic Geometry

Scientific paper

We study the functional codes $C_2(X)$ defined on a projective variety $X$, in the case where $X \subset {\mathbb{P}}^3$ is a non-degenerate hermitian surface. We first give some bounds for $# X_{Z(\mathcal{Q})}(\mathbb{F}_{q})$, 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 $C_2(X)$.

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