The problem of correcting transpositions (or swaps) of consecutive symbols in $ q $-ary strings is studied. Lower bounds on asymptotically achievable rates of codes correcting $ t = τn $ transpositions are derived. The first bound is obtained by analyzing the average cardinality of ``transposition balls'' and evaluating the appropriate version of the generalized Gilbert--Varshamov bound, while the second bound follows from a construction of codes correcting an arbitrary number of transpositions (i.e., zero-error codes). Asymptotic bounds on the cardinality of optimal codes correcting $ t = \textrm{const} $ transpositions are also derived.

翻译：本文研究了在$q$元字符串中纠正连续符号换位（或交换）错误的问题。推导了能够纠正$t = τn$次换位错误的编码的渐近可达速率下界。第一个下界通过分析"换位球"的平均基数并评估广义吉尔伯特-瓦沙莫夫界的适当形式得到，而第二个下界则源于能够纠正任意次数换位错误（即零错误编码）的编码构造。同时推导了纠正$t = \textrm{const}$次换位错误的最优编码基数的渐近界。