Fast decoding of codes from algebraic curves

The author shows how the fast decoding algorithm of Justesen et al. (1989), for codes from algebraic plane curves, can be extended such that codes from curves in an r-dimensional space can be decoded. He shows how Sakata's (1990) Berlekamp-Massey (1969) extension can be used to find an error locator polynomial, and also shows that the cost of doing this increases with the dimension of the space. Unfortunately, the error-correcting capability gets worse for codes from curves in higher dimensional spaces. For a specific curve, he determines the error values faster than by solving linear equations. The method is an extension of the transformation method known from cyclic codes.<
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