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Quadratic-Curve-Lifted Reed-Solomon Codes
- Publication Year :
- 2021
-
Abstract
- 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 show that the asymptotic rate of a QC-LRS code over $\mathbb{F}_q$ with local redundancy $r$ is $1-\Theta(q/r)^{-0.2284}$. 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.<br />Comment: 16 pages, 2 figures. A short version is accepted by WCC 2022 (12th International Workshop on Coding and Cryptography)
- Subjects :
- Computer Science - Information Theory
Mathematics - Algebraic Geometry
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2109.14478
- Document Type :
- Working Paper