论文标题
多数逻辑解码某些Schubert代码使用Schubert品种中的行
Majority Logic Decoding for Certain Schubert Codes Using Lines in Schubert Varieties
论文作者
论文摘要
在本文中，我们考虑了Schubert代码，与Schubert品种相关的线性代码，并讨论了双重舒伯特代码的最小重量代码。仔细观察了Schubert品种中的线条概念，并且已经证明，双舒伯特代码的最小重量代码的支撑位于线上，而Schubert品种中的任何三个点都对应于对Schubert代码的最小重量平价检查的支持。我们在Schubert品种中使用这些行来构建某些Schubert代码的正交奇偶校验检查，并将其用于多数逻辑解码。在某些特殊情况下，我们可以校正大约$ \ lfloor（d-1）/2 \ rfloor $许多错误，其中$ d $是代码的最小距离。
In this article, we consider Schubert codes, linear codes associated to Schubert varieties, and discuss minimum weight codewords for dual Schubert codes. The notion of lines in Schubert varieties is looked closely at, and it has been proved that the supports of the minimum weight codewords of the dual Schubert codes lie on lines and any three points on a line in Schubert variety correspond to the support of some minimum weight parity check for the Schubert code. We use these lines in Schubert varieties to construct orthogonal parity checks for certain Schubert codes and use them for majority logic decoding. In some special cases, we can correct approximately up to $\lfloor (d-1)/2\rfloor$ many errors where $d$ is the minimum distance of the code.
