Determination of error values for decoding hermitian codes with the inverse affine Fourier transform

摘要

With the knowledge of the syndromes S_a,b 0≤a, b≤q-2, the exact error values cannot be determined by using the conventional(q-1)~2-point discrete Fourier transform in the decoding of a plane algebraic-geometric code over GF(q). In this letter, the inverse q-point 1-dimensional and Q~2-point 2- Dimensional affine Fourier transform over GF(q)are presented To be used to retrieve the actual error values, but it requires Much computation efforts. For saving computation complexity, A modification of the affine Fourier transform is derived by using The property of the rational points of the plane Hermitian curve.