New Construction of $q$-ary Codes Correcting a Burst of at most $t$ Deletions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913337620561920 |
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| author | Song, Wentu Cai, Kui Quek, Tony Q. S. |
| author_facet | Song, Wentu Cai, Kui Quek, Tony Q. S. |
| contents | In this paper, for any fixed positive integers $t$ and $q>2$, we construct $q$-ary codes correcting a burst of at most $t$ deletions with redundancy $\log n+8\log\log n+o(\log\log n)+γ_{q,t}$ bits and near-linear encoding/decoding complexity, where $n$ is the message length and $γ_{q,t}$ is a constant that only depends on $q$ and $t$. In previous works there are constructions of such codes with redundancy $\log n+O(\log q\log\log n)$ bits or $\log n+O(t^2\log\log n)+O(t\log q)$. The redundancy of our new construction is independent of $q$ and $t$ in the second term. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_05859 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New Construction of $q$-ary Codes Correcting a Burst of at most $t$ Deletions Song, Wentu Cai, Kui Quek, Tony Q. S. Information Theory In this paper, for any fixed positive integers $t$ and $q>2$, we construct $q$-ary codes correcting a burst of at most $t$ deletions with redundancy $\log n+8\log\log n+o(\log\log n)+γ_{q,t}$ bits and near-linear encoding/decoding complexity, where $n$ is the message length and $γ_{q,t}$ is a constant that only depends on $q$ and $t$. In previous works there are constructions of such codes with redundancy $\log n+O(\log q\log\log n)$ bits or $\log n+O(t^2\log\log n)+O(t\log q)$. The redundancy of our new construction is independent of $q$ and $t$ in the second term. |
| title | New Construction of $q$-ary Codes Correcting a Burst of at most $t$ Deletions |
| topic | Information Theory |
| url | https://arxiv.org/abs/2401.05859 |