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In this paper, for any fixed integer $q>2$, we construct $q$-ary codescorrecting a burst of at most $t$ deletions with redundancy $\log n+8\log\logn+o(\log\log n)+\gamma_{q,t}$ bits and near-linear encoding/decodingcomplexity, where $n$ is the message length and $\gamma_{q,t}$ is a constantthat only depends on $q$ and $t$. In previous works there are constructions ofsuch codes with redundancy $\log n+O(\log q\log\log n)$ bits or $\logn+O(t^2\log\log n)+O(t\log q)$. The redundancy of our new construction isindependent of $q$ and $t$ in the second term.

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