Mapping Quaternary Varshamov-Tenengolts and Helberg Codes to Binary Spaces with Naisargik Images
Naisargik maps from quaternary to binary spaces can enhance the deletion error-correcting capabilities of Varshamov-Tenengolts and Helberg codes.
Optimal List-Decoding of Polynomial Ideal Codes with Efficient Algorithms
Randomly punctured polynomial ideal codes over an exponentially large alphabet exactly achieve the Singleton bound for list-decoding, while those over a polynomially large alphabet approximately achieve it. These codes can also be efficiently list-decoded up to the (approximate) Singleton bound.
Optimal Two-Dimensional Reed-Solomon Codes for Correcting Insertions and Deletions
This paper constructs explicit [n, 2]q Reed-Solomon codes that can correct from n-3 insertion and deletion errors, where the field size q is O(n^3), resolving the minimum field size needed for such codes.
Constructing Asymptotically Good Relaxed Locally Correctable Codes with Polylogarithmic Query Complexity
We construct the first asymptotically good relaxed locally correctable codes with polylogarithmic query complexity, bringing the upper bound polynomially close to the lower bound.
Random Reed-Solomon Codes Achieve List Recovery Capacity with Optimal List Size
Random Reed-Solomon codes are list recoverable up to capacity with optimal output list size, for any input list size.