论文标题
免费的分辨率和二进制线性代码的广义锤击权重
Free Resolutions and Generalized Hamming Weights of binary linear codes
论文作者
论文摘要
在这项工作中，我们探讨了某些单一理想的自由分辨率与二元代码的广义锤击权重（GHW）之间的关系。更确切地说，我们寻找的结构比最小支持的一组代码字要小，这些结构为我们提供了有关GHW的一些信息。我们证明，可以从与代码相关的二项式理想相关的一组单元中计算出二进制线性代码的第一个和第二个广义锤式重量。此外，剩余的权重由该集合的Betti数字界定。
In this work, we explore the relationship between free resolution of some monomial ideals and Generalized Hamming Weights (GHWs) of binary codes. More precisely, we look for a structure smaller than the set of codewords of minimal support that provides us some information about the GHWs. We prove that the first and second generalized Hamming weight of a binary linear code can be computed (by means of a graded free resolution) from a set of monomials associated to a binomial ideal related with the code. Moreover, the remaining weights are bounded by the Betti numbers for that set.
