Affine Cartesian codes with complementary duals
Affine Cartesian codes with complementary duals
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DOI：
10.1016/j.ffa.2019.01.004
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发表时间：
2018-05
期刊：
影响因子：
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通讯作者：
Hiram H. López;Felice Manganiello;Gretchen L. Matthews
中科院分区：
文献类型：
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作者：
Hiram H. López;Felice Manganiello;Gretchen L. Matthews
具有C <$C <$={0}性质的线性码C被称为线性互补对偶码或LCD码。本文研究了一类广义仿射笛卡尔码，它是LCD码.广义仿射笛卡尔码自然地产生为仿射笛卡尔码的逆，其方式与广义里德-所罗门码自然地产生为里德-所罗门码的逆相同。广义仿射笛卡尔码是通过在有限域K上的m维笛卡尔集合中的点处对有界次数的多元多项式求值并缩放坐标而构造的求值码。LCD属性取决于所使用的标量。由于Reed-Solomon码是一种特殊情况，我们得到了广义Reed-Solomon码是LCD的一个特征，沿着广义仿射Cartesian码的更一般的结果。这些结果与下伏场的特性无关。
A linear code C with the property that C∩ C⊥={0} is said to be a linear complementary dual, or LCD, code. In this paper, we consider generalized affine Cartesian codes which are LCD. Generalized affine Cartesian codes arise naturally as the duals of affine Cartesian codes in the same way that generalized Reed–Solomon codes arise as duals of Reed–Solomon codes. Generalized affine Cartesian codes are evaluation codes constructed by evaluating multivariate polynomials of bounded degree at points in an m-dimensional Cartesian set over a finite field K and scaling the coordinates. The LCD property depends on the scalars used. Because Reed–Solomon codes are a special case, we obtain a characterization of those generalized Reed–Solomon codes which are LCD along with the more general result for generalized affine Cartesian codes. These results are independent of the characteristic of the underlying field.