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

2005/12/20 by Frédéric A. B. Edoukou, Frederic A. B. Edoukou, Edoukou, Frederic A. B.
Computer Science · Mathematics · #Coding theory and cryptography #Cooperative Communication and Network Coding #math.AG #msc:05B25 #msc:11T71 #msc:14J29

paper · pdf · doi:10.48550/arxiv.math/0512476

arxiv created 2005/12/20 · arxiv updated 2009/12/01

Abstract

We study the functional codes C₂(X) defined on a projective variety X, in the case where X ⊂ ℙ³ is a non-degenerate hermitian surface. We first give some bounds for # X_Z(Q)(\mathbbF_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 C₂(X).

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