Reed–Solomon Codes over Fields of Characteristic Zero
Carmen Sippel, Cornelia Ott, Sven Puchinger, Martin Bossert · 2019
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.