In this article, we consider the decoding problem of Grassmann codes using majority logic. We show that for two points of the Grassmannian, there exists a canonical geodesic between these points once a complete flag is fixed. These geodesics are used to construct a large set of parity checks orthogonal on a coordinate of the code, resulting in a majority decoding algorithm.

中文翻译：

---

Grassmannian上的点线入射和Grassmann码的多数逻辑解码

在本文中，我们考虑使用多数逻辑对格拉斯曼码进行解码的问题。我们表明，对于格拉斯曼式的两个点，一旦确定了完整的标志，则在这些点之间将存在一个规范的测地线。这些测地线用于构建在代码坐标上正交的大量奇偶校验，从而形成多数解码算法。