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Lower rate
bounds for Hermitian-lifted codes in odd prime
characteristic
Beth Malmskog and Na’ama Nevo |
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Vol. 18 (2025), No. 4, 643–664
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Abstract |
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Locally recoverable codes are error-correcting codes with the additional property that every symbol of any codeword can be recovered from a small set of other symbols. This property is particularly desirable in cloud storage applications. A locally recoverable code is said to have availability if each position has disjoint recovery sets. Hermitian-lifted codes are locally recoverable codes with high availability first described by López, Malmskog, Matthews, Piñero-Gonzáles, and Wootters. The codes are based on the well-known Hermitian curve and incorporate the novel technique of lifting to increase the rate of the code. López et al. (2021) provided a lower bound for the rate of the codes defined over fields with characteristic 2. This paper generalizes their work to show that the rate of Hermitian-lifted codes is bounded below by a positive constant depending on , when for any odd prime . |
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Keywords
Hermitian-lifted codes, locally recoverable codes,
availability, Hermitian curve
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Mathematical Subject Classification
Primary: 11T71, 14G50, 94B27
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Milestones
Received: 28 August 2023
Revised: 29 January 2024
Accepted: 6 March 2024
Published: 30 July 2025
Communicated by Nathan Kaplan
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Authors |
| Beth Malmskog | |
| Mathematics and Computer
Science Colorado College Colorado Springs, CO United States |
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| Na’ama Nevo | |
| Mathematics Northeastern University Boston, MA United States |
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| © 2025 MSP (Mathematical Sciences Publishers). |
