New Construction of $q$-ary Codes Correcting a Burst of at most $t$ Deletions

Fuente: arXiv
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Main Authors: Song, Wentu, Cai, Kui, Quek, Tony Q. S.
Format: Preprint
Published: 2024
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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
id 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