Binary t_1-Deletion-t_2-Insertion-Burst Correcting Codes and Codes Correcting a Burst of Deletions

11/21/2022

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by   Zuo Ye, et al.

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We first give a construction of binary t_1-deletion-t_2-insertion-burst correcting codes with redundancy at most log(n)+(t_1-t_2-1)loglog(n)+O(1), where t_1≥ 2t_2. Then we give an improved construction of binary codes capable of correcting a burst of 4 non-consecutive deletions, whose redundancy is reduced from 7log(n)+2loglog(n)+O(1) to 4log(n)+6loglog(n)+O(1). Lastly, by connecting non-binary b-burst-deletion correcting codes with binary 2b-deletion-b-insertion-burst correcting codes, we give a new construction of non-binary b-burst-deletion correcting codes with redundancy at most log(n)+(b-1)loglog(n)+O(1). This construction is different from previous results.