Reed–Solomon Codes over Fields of Characteristic Zero

  title={Reed–Solomon Codes over Fields of Characteristic Zero},
  author={Carmen Sippel and Cornelia Ott and Sven Puchinger and Martin Bossert},
  journal={2019 IEEE International Symposium on Information Theory (ISIT)},
  • Carmen Sippel, C. Ott, +1 author M. Bossert
  • Published 2019
  • Computer Science, Mathematics
  • 2019 IEEE International Symposium on Information Theory (ISIT)
We study Reed–Solomon codes over arbitrary fields, inspired by several recent papers dealing with Gabidulin codes over fields of characteristic zero. Over the field of rational numbers, we derive bounds on the coefficient growth during encoding and the bit complexity of decoding, which is polynomial in the code length and in the bit width of error and codeword values. The results can be generalized to arbitrary number fields. 


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