This paper studies the cardinality of codes correcting insertions and deletions. We give improved upper and lower bounds on code size. Our upper bound is obtained by utilizing the asymmetric property of list decoding for insertions and deletions and can be seen as analogous to the Elias bound in the Hamming metric. Our non-asymptotic bound is better than the existing bounds when the minimum Levenshtein distance is relatively large. The asymptotic bound exceeds the Elias and the MRRW bounds adapted from the Hamming-metric bounds for the binary and the quaternary cases. Our lower bound improves on the bound by Levenshtein, but its effect is limited and vanishes asymptotically.

翻译：本文研究可纠正插入与删除错误的码的基数。我们给出了码尺寸的改进上下界。上界通过利用列表解码在插入与删除场景下的非对称性质获得，可视为汉明度量中Elias界的类比。当最小莱文斯坦距离较大时，我们的非渐进界优于现有界。在二进制与四进制情形下，渐进界超过了从汉明度量界推广而来的Elias界与MRRW界。下界改进了Levenshtein界，但其影响有限且在渐近意义下消失。