Improved Constructions of Permutation and Multi-Permutation Codes Correcting a Burst of Stable Deletions

Permutation codes and multi-permutation codes have been widely considered due to their various applications, especially in flash memory. In this paper, we consider permutation codes and multi-permutation codes against a burst of stable deletions. In particular, we propose a construction of permutation codes correcting a burst stable deletion of length $s$ , with redundancy $\log n+ 2\log \log n+O(1{)}$ . Compared to the previous known results, our improvement relies on a different strategy to retrieve the missing symbol on the first row of the array representation of a permutation. We also generalize our constructions for multi-permutations and the variable length burst model. Furthermore, we propose a linear-time encoder with optimal redundancy for single stable deletion correcting permutation codes.