Two applications of Weil-Serre's explicit formula

We apply Weil-Serre's explicit formula to produce non-trivial estimates of exponential sums along a curve and of the dual distance of subfield subcodes of algebraic-geometric (AG-)codes. These bounds work while the number of rational points of a curve is large when compared to its genus thus the Weil-Bombieri bound for exponential sums being trivial.Partly supported by Russian Fundamental Research Foundation (project N 93-012-458) and by the grant MPN000 from the International Science FoundationThe author is deeply grateful to Mme Aurélia Lozingot for her help in typing of the present paper.