Metric Structure of Linear Codes and Algebraic-Geometry Codes

We use the study of bilinear forms over a finite field to give a decomposition of the linear codes similar to the one in [10] for generalized toric codes. Such decomposition, called geometric decomposition of a linear code and which can be obtained in a constructive way, allows to express easily the dual of a linear code and gives a method to estimate the minimum distance. The proofs for characteristic 2 are different, but they will be developed parallel. This allows us to obtain a new paradigm to define the family of linear codes. We also study this decomposition for Algebraic