多维拉丁文Bitrade
Multidimensional Latin Bitrade
摘要：
$k$元$n$维超立方体的子集$S$称为拉丁比特，如果对于每个1面$F$有$|S\cap F|\in\{0,2\} $.我们发现所有容许的小（小于$2^{n+1}$）基数拉丁bitrades。$k$ -元$n$ -维超立方体的一个子集$M$称为$t$ -折MDS码，如果对于每个1-面$F$有$|M\cap F|=t $.两个1倍MDS码的对称差总是拉丁比特。两个$t$折叠MDS码的对称差也可以是拉丁比特率。在这种情况下，我们说，这个拉丁bitrade嵌入到$t$倍MDS代码。$t$ -fold MDS码和嵌入其中的拉丁比特率的交集被称为码的分量。我们研究了拉丁比特串嵌入到$t$ -fold MDS中的问题以及$t$ -fold MDS分量的可接受基数。关键词：MDS码，拉丁比特，分量。
英文摘要：
A subset $S$ of $k$-ary $n$-dimensional hypercube is called latin bitrade if $|S\cap F|\in\{0,2\} $ for each 1-face $F$. We find all admissible small (less than $2^{n+1}$) cardinalities of latin bitrades. A subset $M$ of $k$-ary $n$-dimensional hypercube is called $t$-fold MDS code if $|M\cap F|=t $ for each 1-face $F$. Symmetric difference of two 1-fold MDS codes is always a latin bitrade. Symmetric difference of two $t$-fold MDS codes may also be a latin bitrade. In this case we say that this latin bitrade embedded into $t$-fold MDS code. The intersection of $t$-fold MDS code and a latin bitrade embedded into it is called a component of the code. We study the questions of embedding of latin bitrades into $t$-fold MDS and admissible cardinalities of the component of $t$-fold MDS. Keywords: MDS code, latin bitrade, component.
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