论文标题
通过切换构建MRD代码
Constructing MRD codes by switching
论文作者
论文摘要
MRD代码是$ m $ - by- $ n $矩阵上订单$ q $的$ m $ n $矩阵的最大代码。它们的直径是完美的，并且具有基数$ q^{m（n-d+1）} $，如果$ m \ ge n $。我们将MRD代码中的切换定义为用相同参数的其他子代码替换特殊的MRD子代码。我们考虑了承认此类切换的MRD代码的结构，包括刺穿的扭曲的Gabidulin代码和直接产物代码。使用开关，我们构建了一类巨大的MRD代码，如果固定其他参数（$ n $，$ q $，代码距离），其基数将在$ m $中呈指数增长。此外，我们构建具有不同仿射等级和Aperiodic MRD代码的MRD代码。 关键字：MRD代码，等级距离，双线性形式图，切换，直径完美代码
MRD codes are maximum codes in the rank-distance metric space on $m$-by-$n$ matrices over the finite field of order $q$. They are diameter perfect and have the cardinality $q^{m(n-d+1)}$ if $m\ge n$. We define switching in MRD codes as replacing special MRD subcodes by other subcodes with the same parameters. We consider constructions of MRD codes admitting such switching, including punctured twisted Gabidulin codes and direct-product codes. Using switching, we construct a huge class of MRD codes whose cardinality grows doubly exponentially in $m$ if the other parameters ($n$, $q$, the code distance) are fixed. Moreover, we construct MRD codes with different affine ranks and aperiodic MRD codes. Keywords: MRD codes, rank distance, bilinear forms graph, switching, diameter perfect codes
