On Differential Varshamov—Tenengolts Codes

Differential Varshamov-Tenengolts (D-VT) codes, recently introduced by Nguyen et al. (2024), are q-ary codes that can correct a single deletion (or insertion) error with reduced redundancy compared to the Tenengolts q-ary single deletion correction codes. In this work, we completely determine the sizes of D-VT codes. We clarify the relationship between D-VT codes and Tenengolts codes, which implies a more efficient D-VT decoding algorithm. Finally, we present an alternative characterization of certain D-VT codes in terms of q-ary necklaces.