关于半径为1的Levenshtein球
On Levenshtein Balls with Radius One
摘要：
DNA存储技术的快速发展使缺失和插入通道再次成为研究的前沿。当删除的数量等于插入的数量时，固定长度Levenshtein（FLL）度量是两个相同长度的单词之间距离的正确度量。球的大小是任何度量中最基本的参数之一。在FLL度量中半径为1的球的大小取决于游程的数量和给定单词的交替段的长度。在这项工作中，我们发现的最小值，最大值和平均大小的球半径为1，在FLL度量。并计算了具有直径1的最大反码的最小和最大码长。
英文摘要：
The rapid development of DNA storage has brought the deletion and insertion channel, once again, to the front line of research. When the number of deletions is equal to the number of insertions, the Fixed Length Levenshtein (FLL) metric is the right measure for the distance between two words of the same length. The size of a ball is one of the most fundamental parameters in any metric. The size of the ball with radius one in the FLL metric depends on the number of runs and the length of the alternating segments of the given word. In this work, we find the minimum, maximum, and average size of a ball with radius one, in the FLL metric. The related minimum and maximum sizes of a maximal anticode with diameter one are also calculated.
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