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.

本文研究了纠正插入和删除的代码基数。我们给出了代码大小的改进上限和下限。我们的上限是通过利用列表解码的不对称特性来进行插入和删除而获得的，并且可以被视为类似于汉明度量中的 Elias 界限。当最小 Levenshtein 距离相对较大时，我们的非渐近边界优于现有边界。对于二元和四元情况，渐近边界超过了 Elias 和改编自汉明度量边界的 MRRW 边界。我们的下界改进了 Levenshtein 的界限，但其效果有限并且渐近消失。