This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation encoding is the right choice for these codes and then we provide easily reversible encoding methods for each family. Later unique decoding algorithms for the codes are described. The decoding algorithms are interpolation-based and can uniquely correct errors for each code with rank up to $\lfloor(d-1)/2\rfloor$ in polynomial-time, where $d$ is the minimum distance of the code.

翻译：本文介绍了一些最优等级的通用代码家庭的编码和解码算法,其代码以限制性的对称、交替和埃米提亚矩阵形式出现。 首先,我们显示评价编码是这些代码的正确选择,然后我们为每个家庭提供容易反转的编码方法。 本文介绍了后来这些代码的独特解码算法。 解码算法基于内插,可以独有地纠正每个代码的错误,其等级在多元米亚时为$\l底(d-1)/2美元/r底值,其中美元是代码的最低距离。