Paper 2023/824 Original: eprint.iacr.org/2023/824 ↗
Reed-Solomon Codes over the Circle Group
Abstract
In this note we discuss Reed-Solomon codes with domain of definition within the unit circle of the complex extension $\mathbb C(F)$ of a Mersenne prime field $F$. Within this unit circle the interpolants of “real”, i.e. $F$-valued, functions are again almost real, meaning that their values can be rectified to a real representation at almost no extra cost. Second, using standard techniques for the FFT of real-valued functions, encoding can be sped up significantly. Due to the particularly efficient arithmetic of Mersenne fields, we expect these “almost native” Reed-Solomon codes to perform as native ones based on prime fields with high two-adicity, but less processor-friendly arithmetic.
Metadata
- Available format(s)
PDF- Category
- Applications
- Publication info
- Preprint.
- History
- 2023-06-02: last updated
- 2023-06-02: published
- Short URL
- https://ia.cr/2023/824
- License
- https://creativecommons.org/licenses/by-sa/4.0/
BibTeX
@misc{cryptoeprint:2023/824,
author = {Ulrich Haböck and Daniel Lubarov and Jacqueline Nabaglo},
title = {Reed-Solomon Codes over the Circle Group},
howpublished = {Cryptology {ePrint} Archive, Paper 2023/824},
year = {2023},
url = {https://eprint.iacr.org/2023/824}
}