Codes Correcting Two Bursts of Exactly $b$ Deletions

Abstract

In this paper, we explore constructions for codes that correct two bursts of deletions, with each burst having length exactly $b$. Previously, the best known construction, derived using the syndrome compression technique, achieved a redundancy of at most $7\log n+O\left(\log n/\log\log n\right)$. In this work, we present new constructions for all $q\ge 2$ that achieve redundancy at most $7\log n+O(\log\log n)$ when $b>1$. Additionally, for $b=1$, we provide a new construction of $q$-ary two-deletion correcting codes with redundancy $5\log n+O(\log\log n)$ for all $q>2$.