In this work we consider linear codes which are locally testable
in a sublinear number of queries. We give the first general family
of locally testable codes of exponential size. Previous results of
this form were known only for codes of quasi-polynomial size (e.g.
Reed-Muller codes). We accomplish this by ... more >>>

The Stepanov-Bombieri proof of the Hasse-Weil bound also gives non-trivial bounds on the bias of character sums over curves with small genus, for any low-degree function $f$ that is not completely biased. For high genus curves, and in particular for curves used in AG codes over constant size fields, the ... more >>>