The aim of this work is to give degree formulas for the generalized Hamming weights of evaluation codes and to show lower bounds for these weights. In particular, we give degree formulas for the generalized Hamming weights of Reed--Muller-type codes, and we determine the minimum distance of toric codes over hypersimplices, and the 1st and 2nd generalized Hamming weights of squarefree evaluation codes.

中文翻译：

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评价代码及其基本参数

这项工作的目的是给出评估代码的广义汉明权重的度公式，并显示这些权重的下限。特别地，我们给出了Reed--Muller型码的广义汉明权重的度公式，并确定了复曲面码在超单纯上的最小距离，以及squarefree评估码的一阶和二阶广义汉明权重。