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Greedy weights for matroids
Designs, Codes and Cryptography ( IF 1.6 ) Pub Date : 2020-12-19 , DOI: 10.1007/s10623-020-00824-w
Trygve Johnsen , Hugues Verdure

We introduce greedy weights of matroids, inspired by those for linear codes. We show that a Wei duality holds for two of these types of greedy weights for matroids. Moreover we show that in the cases where the matroids involved are associated to linear codes, our definitions coincide with those for codes. Thus our Wei duality is a generalization of that for linear codes given by Schaathun. In the last part of the paper we show how some important chains of cycles of the matroids appearing, correspond to chains of component maps of minimal resolutions of the independence complex of the corresponding matroids. We also relate properties of these resolutions to chainedness and greedy weights of the matroids, and in many cases codes, that appear.

中文翻译:

拟阵的贪婪权重

我们引入了拟阵的贪婪权重,其灵感来自于线性码。我们证明了 Wei 对偶性适用于拟阵的这两种类型的贪婪权重。此外,我们表明,在所涉及的拟阵与线性代码相关联的情况下,我们的定义与代码的定义一致。因此,我们的 Wei 对偶性是 Schaathun 给出的线性码的推广。在论文的最后一部分,我们展示了一些重要的拟阵循环链是如何对应于对应拟阵的独立复数的最小分辨率的分量映射链的。我们还将这些分辨率的属性与拟阵的链式和贪婪权重相关联,在许多情况下,出现的代码。
更新日期:2020-12-19
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