On the Size of Levenshtein Balls
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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 Levenshtein 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. In this work, the minimum, maximum, and average size of a ball with radius one, in the Levenshtein metric, is considered. The related minimum and maximum size of a maximal anticode with diameter one is also calculated.
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