Codes Defined by Forms of Degree $2$ on Quadric Surfaces
Codes Defined by Forms of Degree $2$ on Quadric Surfaces
复制标题
由二次曲面上 $2$ 次数形式定义的代码
DOI：
10.1109/tit.2007.913450
复制
发表时间：
2005
影响因子：
2.5
通讯作者：
Frédéric A. B. Edoukou
中科院分区：
文献类型：
--
作者：
Frédéric A. B. Edoukou
本文研究了X下标P3（Fq）是1-简并二次曲面或非简并二次曲面（双曲型或椭圆型）时，定义在射影变体X上的功能码C2(X)。我们找到这些代码的最小距离，第二个权值，和第三个权值。我们还展示了第一权重码字和第二权重码字的几何结构。根据A. E. browwer的表，证明了椭圆二次曲面上定义的码C2(X)是好码。
In this correspondence, we study the functional codes C2(X) defined on projective varieties X, in the case where X sub P3(Fq) is a 1-degenerate quadric or a nondegenerate 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 C2(X) defined on the elliptic quadrics are good codes according to the table of A. E. Brouwer.