论文标题
改进对称级别度量错误的解码
Improved decoding of symmetric rank metric errors
论文作者
论文摘要
假设误差矩阵是对称的，我们考虑了秩公式代码的解码。我们证明了两个结果。首先，对于$ <1/2 $的费率，存在一个广泛的等级度量代码的家庭，即任何对称误差模式，即使是最大等级也可以纠正。此外，相应的可解码代码系列包括$ <1/2 $的速率代码。其次，对于$> 1/2 $的价格，我们建议使用Gabidulin代码的解码器纠正对称排名的对称错误，最高为$ n-k $。提到的两个解码器是确定性和最坏情况。
We consider the decoding of rank metric codes assuming the error matrix is symmetric. We prove two results. First, for rates $<1/2$ there exists a broad family of rank metric codes for which any symmetric error pattern, even of maximal rank can be corrected. Moreover, the corresponding family of decodable codes includes Gabidulin codes of rate $<1/2$. Second, for rates $>1/2$, we propose a decoder for Gabidulin codes correcting symmetric errors of rank up to $n-k$. The two mentioned decoders are deterministic and worst case.
