# Reed-Solomon Codes over Fields of Characteristic Zero

## TL;DR

This paper investigates Reed-Solomon codes over fields of characteristic zero, providing bounds on coefficient growth and decoding complexity, with potential generalizations to other number fields.

## Contribution

It extends Reed-Solomon code analysis to characteristic zero fields, deriving bounds on encoding growth and decoding complexity, inspired by recent work on Gabidulin codes.

## Key findings

- Bounds on coefficient growth during encoding
- Polynomial bit complexity of decoding
- Generalization to arbitrary number fields

## Abstract

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.