Reed-Solomon Codes over Fields of Characteristic Zero

01/21/2019

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by   Carmen Sippel, et al.

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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 bitsize of the error values. The results can be generalized to arbitrary number fields.