Encoding via Gr\"obner bases and discrete Fourier transforms for several types of algebraic codes
<|reference_start|>Encoding via Gr\"obner bases and discrete Fourier transforms for several types of algebraic codes: We propose a novel encoding scheme for algebraic codes such as codes on algebraic curves, multidimensional cyclic codes, and hyperbolic cascaded Reed-Solomon codes and present numerical examples. We employ the recurrence from the Gr\"obner basis of the locator ideal for a set of rational points and the two-dimensional inverse discrete Fourier transform. We generalize the functioning of the generator polynomial for Reed-Solomon codes and develop systematic encoding for various algebraic codes.<|reference_end|>
@article{matsui2007encoding,
    title={Encoding via Gr\"obner bases and discrete Fourier transforms for several
  types of algebraic codes},
    author={Hajime Matsui, Seiichi Mita},
    journal={arXiv preprint arXiv:cs/0703104},
    year={2007},
    archivePrefix={arXiv},
    eprint={cs/0703104},
    primaryClass={cs.IT math.IT}
}