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：本文研究插入与删除纠错码的码字容量。我们给出了码字规模的上界和下界的改进。上界通过利用插入与删除的列表解码的非对称性质获得，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，我们的非渐近界优于现有界。对于二进制和四进制情形，渐近界超过了从汉明度量界改编而来的Elias界和MRRW界。下界改进了Levenshtein界，但其效果有限且渐近消失。