Codes Defined By Forms Of Degree 2 On Quadric Surfaces

Details Codes Defined By Forms Of Degree 2 On Quadric Surfaces Codes Defined By Forms Of Degree 2 On Quadric Surfaces

2005-11-28

arxiv.org/abs/math/0511679v1

Mathematics

Algebraic Geometry

submitted to IEEE, November 25, 2005

Scientific paper

We study the functional codes $C_2(X)$ defined on projective varieties $X$, in the case where $X\subset \mathbb{P}^3$ is a 1-degenerate quadric or a non-degenerate quadric (hyperbolic or elliptic). We find the minimum distance of these codes, the second weight, and the third weight. We also show the geometrical structure of the first weight and second weight codewords. One result states that the codes $C_2(X)$ defined on the elliptic quadrics are good codes according to the table of A. E. Brouwer.

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