  An efficient procedure for error-value calculations based on fast discrete
Fourier transforms (DFT) in conjunction with Berlekamp-Massey-Sakata algorithm
for a class of affine variety codes is proposed. Our procedure is achieved by
multidimensional DFT and linear recurrence relations from Grobner basis and is
applied to erasure-and-error decoding and systematic encoding. The
computational complexity of error-value calculations in our algorithm improves
that in solving systems of linear equations from error correcting pairs in many
cases. A motivating example of our algorithm in case of a Reed-Solomon code and
a numerical example of our algorithm in case of a Hermitian code are also
described.
