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

• LIU Chih-Wei

  the Communication Science Research LAB., Department of Electrical Engineering, National Tsing Hua University

Abstract

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>.

Journal

• IEICE transactions on fundamentals of electronics, communications and computer sciences

  IEICE transactions on fundamentals of electronics, communications and computer sciences 82 (10), 2302-2305, 1999-10-25

  The Institute of Electronics, Information and Communication Engineers

Keywords

• algebraic-geometric code
• Hermitian code
• affine Fourier transform
• error valve

Details

• CRID: 1572824502217545728
• NII Article ID: 110003208168
• NII Book ID: AA10826239
• ISSN: 09168508
• Text Lang: en
• Data Source:
  • CiNii Articles