论文标题
长度为5和6的三变量代码的最大基数
The maximum cardinality of trifferent codes with lengths 5 and 6
论文作者
论文摘要
代码$ \ MATHCAL {C} \ subseteq \ {0，1，2 \}^n $被认为对长度$ n $是微不足道的，而对于任何三个不同的$ \ Mathcal {C} $的元素都存在一个坐标。将$ \ Mathcal {t}（n）$定义为具有长度$ n $，$ \ MATHCAL {t}（n）$的三变量代码的最大基数，对于$ n \ ge 5 $而言是未知的。在本说明中，我们使用优化的搜索算法表明$ \ Mathcal {t}（5）= 10 $和$ \ Mathcal {t}（6）= 13 $。
A code $\mathcal{C} \subseteq \{0, 1, 2\}^n$ is said to be trifferent with length $n$ when for any three distinct elements of $\mathcal{C}$ there exists a coordinate in which they all differ. Defining $\mathcal{T}(n)$ as the maximum cardinality of trifferent codes with length $n$, $\mathcal{T}(n)$ is unknown for $n \ge 5$. In this note, we use an optimized search algorithm to show that $\mathcal{T}(5) = 10$ and $\mathcal{T}(6) = 13$.
