Improved constructions of permutation and multi-permutation codes correcting a burst of stable deletions

Permutation codes and multi-permutation have been widely considered due to their various applications, especially in flash memory. In this paper, we consider permutation against a burst of stable deletions. particular, propose construction correcting deletion length s , with redundancy log xmlns:xlink="http://www.w3.org/1999/xlink">n + 2 xmlns:xlink="http://www.w3.org/1999/xlink">O (1). Compared the previous known results, our improvement relies on different strategy retrieve missing symbol first row array representation permutation. We also generalize constructions for multi-permutations variable model. Furthermore, linear-time encoder optimal single codes.