论文标题
非二进制二线校正代码和爆发删除校正代码
Non-binary Two-Deletion Correcting Codes and Burst-Deletion Correcting Codes
论文作者
论文摘要
在本文中，我们构建了系统的$ q $ - y-ary两删除校正代码和爆发删除校正代码，其中$ q \ geq 2 $是整数。对于两台式代码，我们的构造具有冗余$ 5 \ log n+o（\ log q \ log \ log n）$，并且在$ n $中编码复杂性接近线性，其中$ n $是消息序列的长度。对于爆发删除代码，我们首先介绍具有冗余$ \ log n+9 \ log \ log \ log \ log n+γ_t+o（\ log \ log \ log n）$ bits $（γ_T$仅取决于$ t）$的常数，并且能够在最多$ t $ t $ deletions use leniz-ipoleanz-poleniz-lenz-iiikie leniz-iikikikii insk-leniz-iikii leniz-iiki，然后，我们为具有冗余$ \ log n+（8 \ log q+9）\ log \ log \ log \ log n+o（\ log q \ log \ log \ log \ log n）+γ_t$ bits进行$ q $ - arive代码的构造，并能够在最多$ t $ deletions纠正一爆。
In this paper, we construct systematic $q$-ary two-deletion correcting codes and burst-deletion correcting codes, where $q\geq 2$ is an even integer. For two-deletion codes, our construction has redundancy $5\log n+O(\log q\log\log n)$ and has encoding complexity near-linear in $n$, where $n$ is the length of the message sequences. For burst-deletion codes, we first present a construction of binary codes with redundancy $\log n+9\log\log n+γ_t+o(\log\log n)$ bits $(γ_t$ is a constant that depends only on $t)$ and capable of correcting a burst of at most $t$ deletions, which improves the Lenz-Polyanskii Construction (ISIT 2020). Then we give a construction of $q$-ary codes with redundancy $\log n+(8\log q+9)\log\log n+o(\log q\log\log n)+γ_t$ bits and capable of correcting a burst of at most $t$ deletions.
