论文标题
Grassmannian $ G_ {2，M} $的轨道结构和Grassmann代码的解码器$ C（2，M）$
Orbit Structure of Grassmannian $G_{2, m}$ and a decoder for Grassmann code $C(2, m)$
论文作者
论文摘要
在本手稿中，我们考虑解码格拉曼法规，即仿射空间中与平面的格拉曼尼亚相关的线性代码。我们看一下由于某些有限场扩展的乘法群体的自然作用而产生的硕士轨道结构。我们将相应的Grassmann代码投影到这些轨道上，以获取某些Reed-Solomon代码的一些子代码。我们证明，其中一些预测的代码包含家长Grassmann代码的信息集。通过提高彼得森对预计子代码的解码算法的效率，我们证明人们可以校正多达$ \ lfloor d-1/2 \ rfloor $ $ d $，其中$ d $是Grassmann代码的最小距离。
In this manuscript, we consider decoding Grassmann codes, linear codes associated to Grassmannian of planes in an affine space. We look at the orbit structure of Grassmannian arising from the natural action of multiplicative group of certain finite field extension. We project the corresponding Grassmann code onto these orbits to obtain a few subcodes of certain Reed-Solomon code. We prove that some of these projected codes contains an information set of the parent Grassmann code. By improving the efficiency of Peterson's decoding algorithm for the projected subcodes, we prove that one can correct up to $\lfloor d-1/2\rfloor$ errors for Grassmann code, where $d$ is the minimum distance of Grassmann code.
