论文标题
超图像和无方形仿射评估代码的曲曲面代码的广义锤子权重
Generalized Hamming weights of toric codes over hypersimplices and square-free affine evaluation codes
论文作者
论文摘要
令$ \ mathbb {f} _ {q} $为有限字段，$ q $元素，其中$ q $是Prime $ p $的功率。如果$ \ mathbb {f} _ {q} $上的多项式是无平方的，那么它的所有单元都不是平方的。在本说明中，我们确定仿射圆环$ t =（\ Mathbb {f} _ {q}^{*}）^{s} $的上限这些多项式。采用结果，我们部分获得了在\ cite {hyper}中定义的超图像和无平方评估代码上的曲曲面代码的广义锤子权重。最后，我们获得了相对于欧几里得标量产品的这些曲折代码的双重代码。
Let $\mathbb{F}_{q}$ be a finite field with $q$ elements, where $q$ is a power of prime $p$. A polynomial over $\mathbb{F}_{q}$ is square-free if all its monomials are square-free. In this note, we determine an upper bound on the number of zeroes in the affine torus $T=(\mathbb{F}_{q}^{*})^{s}$ of any set of $r$ linearly independent square-free polynomials over $\mathbb{F}_{q}$ in $s$ variables, under certain conditions on $r$, $s$ and degree of these polynomials. Applying the results, we partly obtain the generalized Hamming weights of toric codes over hypersimplices and square-free evaluation codes, as defined in \cite{hyper}. Finally, we obtain the dual of these toric codes with respect to the Euclidean scalar product.
