Codes Correcting Two Deletions

Abstract

In this paper, we investigate the problem of constructing codes capable of correcting two deletions. In particular, we construct a code that requires redundancy approximately 8 log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> n + O(log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> n) bits of redundancy, where n denotes the length of the code. To the best of the authors' knowledge, this represents the best known construction in that it requires the lowest number of redundant bits for a code correcting two deletions.