Quadratic-Curve-Lifted Reed-Solomon Codes [article]

Hedongliang Liu, Lukas Holzbaur, Nikita Polyanskii, Sven Puchinger, Antonia Wachter-Zeh
2022 arXiv   pre-print
Lifted codes are a class of evaluation codes attracting more attention due to good locality and intermediate availability. In this work we introduce and study quadratic-curve-lifted Reed-Solomon (QC-LRS) codes, where the codeword symbols whose coordinates are on a quadratic curve form a codeword of a Reed-Solomon code. We first develop a necessary and sufficient condition on the monomials which form a basis the code. Based on the condition, we give upper and lower bounds on the dimension and
more » ... w that the asymptotic rate of a QC-LRS code over 𝔽_q with local redundancy r is 1-Θ(q/r)^-0.2284. Moreover, we provide analytical results on the minimum distance of this class of codes and compare QC-LRS codes with lifted Reed-Solomon codes by simulations in terms of the local recovery capability against erasures. For short lengths, QC-LRS codes have better performance in local recovery for erasures than LRS codes of the same dimension.
arXiv:2109.14478v3 fatcat:5tfk7y5ibzfbdovvhl3sgghjh4