Quadratic Forms, Generalized Hamming Weights of Codes and Curves with Many Points Original Research Article

Words in certain binary trace codes correspond to algebraic curves over finite fields of characteristic 2 and correspond to quadratic forms over image2. Via the relation ?with quadratic forms we construct subcodes in which all non-zero words have minimum weight. We show how the relation between quadratic forms, codes and curves can be used to construct curves with many rational points.