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

Frédéric A. B. Edoukou^{[1]}

- [1] CNRS, Institut de Mathématiques de Luminy Luminy case 907 13288 Marseille Cedex 9 - France

Journal de Théorie des Nombres de Bordeaux (2009)

- Volume: 21, Issue: 1, page 131-143
- ISSN: 1246-7405

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topEdoukou, Frédéric A. B.. "The weight distribution of the functional codes defined by forms of degree 2 on Hermitian surfaces." Journal de Théorie des Nombres de Bordeaux 21.1 (2009): 131-143. <http://eudml.org/doc/10866>.

@article{Edoukou2009,

abstract = {We study the functional codes $C_2(X)$ defined on a projective algebraic variety $X$, in the case where $X \subset \{\mathbb\{P\}\}^3(\mathbb\{F\}_\{q\})$ 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 $C_2(X)$.},

affiliation = {CNRS, Institut de Mathématiques de Luminy Luminy case 907 13288 Marseille Cedex 9 - France},

author = {Edoukou, Frédéric A. B.},

journal = {Journal de Théorie des Nombres de Bordeaux},

keywords = {functional codes; minimum distance; weight distribution},

language = {eng},

number = {1},

pages = {131-143},

publisher = {Université Bordeaux 1},

title = {The weight distribution of the functional codes defined by forms of degree 2 on Hermitian surfaces},

url = {http://eudml.org/doc/10866},

volume = {21},

year = {2009},

}

TY - JOUR

AU - Edoukou, Frédéric A. B.

TI - The weight distribution of the functional codes defined by forms of degree 2 on Hermitian surfaces

JO - Journal de Théorie des Nombres de Bordeaux

PY - 2009

PB - Université Bordeaux 1

VL - 21

IS - 1

SP - 131

EP - 143

AB - We study the functional codes $C_2(X)$ defined on a projective algebraic variety $X$, in the case where $X \subset {\mathbb{P}}^3(\mathbb{F}_{q})$ 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 $C_2(X)$.

LA - eng

KW - functional codes; minimum distance; weight distribution

UR - http://eudml.org/doc/10866

ER -

## References

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