Codes Correcting Two Bursts of Exactly b Deletions

In this paper, we investigate codes designed to correct two bursts of deletions, where each burst has a length of exactly b, where b > 1. The previous best construction, achieved through the syndrome compression technique, had a redundancy of at most 7 log n+O (log n/ log log n) bits. In contrast, our work introduces a novel approach for constructing q-ary codes that attain a redundancy of at most 5 log n + O(log log n) bits for all b > 1 and q ≥ 2. Additionally, for the case where b = 1, we present a new construction of q-ary two-deletion correcting codes with a redundancy of 5 log n + O(log log n) bits, for all q > 2.