MEGA 2007 Effective Methods in Algebraic Geometry Strobl, Austria, June 25th - 29th http://www.ricam.oeaw.ac.at/mega2007

Abstract

Title	Metric structure of linear codes and algebraic-geometry codes
Keywords	Linear codes, finite geometry, algebraic-geometry codes
Abstract	We use the study of bilinear forms over a finite field to give a decomposition of the linear codes similar to the one in [ArXiv:cs.IT/0611010] 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 Geometry Codes.

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