论文标题
二进制$ t_1 $ -deletion- $ t_2 $ - 插入式纠正代码和校正删除爆发的代码
Binary $t_1$-Deletion-$t_2$-Insertion-Burst Correcting Codes and Codes Correcting a Burst of Deletions
论文作者
论文摘要
We first give a construction of binary $t_1$-deletion-$t_2$-insertion-burst correcting codes with redundancy at most $\log(n)+(t_1-t_2-1)\log\log(n)+O(1)$, where $t_1\ge 2t_2$.然后，我们提供了改进的二进制代码的构造，能够纠正$ 4 $非连续删除的爆发，其冗余从$ 7 \ log（n）+2 \ log \ log \ log \ log \ log \ log \ log \ log \ log \ o（n）+o（1）$（$ 4 \ log（log log（n）+6 \ log log \ log \ log \ log \ log \ log（n）+o（1）$（1）$。最后，通过将非二进制$ b $ - 爆炸性纠正代码与二进制$ 2B $ -DETEMTION- $ B $ -B $ -B $ - 插入式纠正校正代码，我们为最多$ \ log（n）+（b-1）+log \ log \ log \ log（n）+（1）的非二进制$ b $ b $ burst-bubrst-demention校正代码进行了新的构造。这种结构与以前的结果不同。
We first give a construction of binary $t_1$-deletion-$t_2$-insertion-burst correcting codes with redundancy at most $\log(n)+(t_1-t_2-1)\log\log(n)+O(1)$, where $t_1\ge 2t_2$. Then we give an improved construction of binary codes capable of correcting a burst of $4$ non-consecutive deletions, whose redundancy is reduced from $7\log(n)+2\log\log(n)+O(1)$ to $4\log(n)+6\log\log(n)+O(1)$. 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 $\log(n)+(b-1)\log\log(n)+O(1)$. This construction is different from previous results.
