Welcome to the resource topic for 2023/824
Title:
Reed-Solomon Codes over the Circle Group
Authors: Ulrich Haböck, Daniel Lubarov, Jacqueline Nabaglo
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.
ePrint: https://eprint.iacr.org/2023/824
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