This is a research-expository paper. It deals with
complexity issues in the theory of linear block codes. The main
emphasis is on the theoretical performance limits of the
best known codes. Therefore, the main subject of the paper are
families of asymptotically good codes, i.e., codes whose rate and
relative ... more >>>

We continue the study of list recovery properties of high-rate tensor codes, initiated by Hemenway, Ron-Zewi, and Wootters (FOCS'17). In that work it was shown that the tensor product of an efficient (poly-time) high-rate globally list recoverable code is {\em approximately} locally list recoverable, as well as globally list recoverable ... more >>>

The Gilbert--Varshamov (GV) bound is a classical existential result in coding theory. It implies that a random linear binary code of rate $\varepsilon^2$ has relative distance at least $\frac{1}{2} - O(\varepsilon)$ with high probability. However, it is a major challenge to construct explicit codes with similar parameters.

One hope to ... more >>>

One of the oldest problems in coding theory is to match the Gilbert--Varshamov bound with explicit binary codes. Over larger---yet still constant-sized---fields, algebraic-geometry codes are known to beat the GV bound. In this work, we leverage this phenomenon by taking traces of AG codes. Our hope is that the margin ... more >>>