Non-binary Two-Deletion Correcting Codes and Burst-Deletion Correcting Codes

10/25/2022

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by   Wentu Song, et al.

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In this paper, we construct systematic 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 5log n+O(log qloglog 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+9loglog n+γ_t+o(loglog n) bits (γ_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+(8log q+9)loglog n+o(log qloglog n)+γ_t bits and capable of correcting a burst of at most t deletions.