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An FGLM method for decoding linear codes

A new algorithmic method is presented for the decoding process of a linear code. This method has the flavor of the FGLM techniques that belong to the framework of the Gröbner Bases Theory. This method consists of two algorithms, one for the preparation phase of the code, and the other one for the decoding process. Starting from a parity check matrix of the linear code, our approach enables the user to decode a given codeword in a number of steps proportional to its length. Complexity analysis, complete examples and comments about the application of FGLM techniques to linear codes are also given in this paper.