2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67677We discuss a class of binary cyclic codes and their dual codes. The minimum distance is determined using algebraic geometry, and an application of Weil's theorem. We relate the weights appearing in the dual codes to the number of rational points on a family of genus 2 curves over a finite field.Number TheoryCombinatorics94B27, 11T71, 14H10, 94B15text