New Construction of $q$-ary Codes Correcting a Burst of at most $t$ Deletions

Abstract

In this paper, for any fixed positive integers $t$ and $q>2$, we construct $q$-ary codes correcting a burst of at most $t$ deletions with redundancy $\log n+8\log \log n+o(\log \log n)+{\gamma }_{q,t}$ bits and near-linear encoding/decoding complexity, where $n$ is the message length and ${\gamma }_{q,t}$ is a constant that only depends on $q$ and $t$. In previous works there are constructions of such codes with redundancy $\log n+O(\log q\log \log n)$ bits or $\log n+O(t^2\log \log n)+O(t\log q)$. The redundancy of our new construction is independent of $q$ and $t$ in the second term.