论文标题
纯分辨率，线性代码和Betti编号
Pure Resolutions, Linear Codes, and Betti Numbers
论文作者
论文摘要
我们考虑了与线性代码相关的Stanley-Reisner环的最小自由分辨率，并给出了具有纯分辨率的线性代码的内在表征。我们使用这种表征来快速推断出与MDS代码相关的Stanley-Reisner环以及恒定重量代码的最低免费分辨率。我们还推断出一阶的芦苇穆勒代码的一阶史丹利 - 赖斯纳环的最低免费分辨率是纯净的，并明确描述了贝蒂数字。此外，我们表明，在高阶芦苇毛刺代码的情况下，最小的免费分辨率几乎总是不纯净的。还确定了与几类两类重量代码相对应的史丹利 - 赖斯纳环的最小自由分辨率的性质，除了第一阶reed-muller代码外，还确定了。
We consider the minimal free resolutions of Stanley-Reisner rings associated to linear codes and give an intrinsic characterization of linear codes having a pure resolution. We use this characterization to quickly deduce the minimal free resolutions of Stanley-Reisner rings associated to MDS codes as well as constant weight codes. We also deduce that the minimal free resolutions of Stanley-Reisner rings of first order Reed-Muller codes are pure, and explicitly describe the Betti numbers. Further, we show that in the case of higher order Reed-Muller codes, the minimal free resolutions are almost always not pure. The nature of the minimal free resolution of Stanley-Reisner rings corresponding to several classes of two-weight codes, besides the first order Reed-Muller codes, is also determined.
