Correction: Reed Solomon Codes Against Adversarial Insertions and Deletions (IEEE Transactions on Information Theory (2023) 69:5 (2991-3000) DOI: 10.1109/TIT.2023.3237711)

The purpose of this note is to correct an error made by Con et al. (2023), specifically in the proof of Theorem 9. Here we correct the proof but as a consequence we get a slightly weaker result. In Theorem9, we claimed that for integers k and n such that k < n/9, there exists an [n,k]_q RS code that can decode from n - 2k + 1 insdel errors where (Formula presented). Here we prove the following. Theorem 1: For integers n and k < n/9, there exists an [n,k]_q RS-code, where (Formula presented) is a prime power, that can decode from n - 2k + 1 adversarial insdel errors. Note that the exponent of n is 4k - 3 whereas in Theorem 9 it is 4k - 4. For constant dimensional codes, the field size is of order O(n^4k-3) , and in particular, for k = 2 the field size is of order O(n⁵) .