Determination of Error Values for Decoding Hermitian Codes with the Inverse Affine Fourier Transform

概要

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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. The modified transform, which has almost the same computation complexity of the conventional discrete Fourier transform, requires the knowledge of syndromes S_<a,b>, 0<__-a,b<__-q-2, and three more extended sytadromes S_<q-1>,S_<0,q-1>,S_<q-1,0>.
社団法人電子情報通信学会の論文
1999-10-25