We present error-correcting codes that achieve the information-theoretically best possible trade-off between the rate and error-correction radius. Specifically, for every 0 < R...
Algebraic codes that achieve list decoding capacity were recently constructed by a careful "folding" of the Reed-Solomon code. The "low-degree" nature of this f...
For every 0 < R < 1 and > 0, we present an explicit construction of error-correcting codes of rate R that can be list decoded in polynomial time up to a fraction (1 - R ...
Abstract. We consider the problem of increasing the threshold parameter of a secret-sharing scheme after the setup (share distribution) phase, without further communication between...