Abstract
In this paper, we construct q-ary two-deletion correcting codes and burst-deletion correcting codes, where q = 2 is an even integer. For two-deletion codes, our construction has redundancy 5 log n + O(log q log log n) and has encoding complexity near-linear in n, where n is the length of the message sequences. For burst-deletion codes, we first present a construction of binary codes with redundancy log n + 9 log log n + ?(t) + o(log log n) bits (?(t) is a constant that depends only on t) and capable of correcting a burst of at most t deletions, which improves the Lenz-Polyanskii Construction (ISIT 2020). Then we give a construction of q-ary codes with redundancy log n + (8 log q + 9) log log n + ?(t) + o(log log n) bits and capable of correcting a burst of at most t deletions.