Codes Correcting Two Bursts of Exactly $b$ Deletions
<|reference_start|>Codes Correcting Two Bursts of Exactly $b$ Deletions: In this paper, we investigate codes designed to correct two bursts of deletions, where each burst has a length of exactly $b$, where $b>1$. The previous best construction, achieved through the syndrome compression technique, had a redundancy of at most $7\log n+O\left(\log n/\log\log n\right)$ bits. In contrast, our work introduces a novel approach for constructing $q$-ary codes that attain a redundancy of at most $5\log n+O(\log\log n)$ bits for all $b>1$ and $q\ge2$. Additionally, for the case where $b=1$, we present a new construction of $q$-ary two-deletion correcting codes with a redundancy of $5\log n+O(\log\log n)$ bits, for all $q>2$.<|reference_end|>
@article{ye2024codes,
    title={Codes Correcting Two Bursts of Exactly $b$ Deletions},
    author={Zuo Ye, Yubo Sun, Wenjun Yu, Gennian Ge and Ohad Elishco},
    journal={arXiv preprint arXiv:2408.03113},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.03113},
    primaryClass={cs.IT math.IT}
}