Property testing considers the task of testing rapidly (with very few samples into the data) if some massive data satisfies a given property, or is far from satisfying the property. This is currently a central topic in computer science. Among the most important are the algebraic properties of polynomial maps, which are affine invariant. This leads and reduces to the study of the weight distribution of dual trace codes of algebraic codes. The key is to obtain good estimates of exponential sums going beyond Weil's bound (the Riemann hypothesis over finite fields). This raises deep new mathematical questions to be explored. In this lecture, I will try to give a self-contained expository introduction, leading up to recent improvements of Weil's bound for exponential sums.