New constructions of optimal \((r, \delta)\)-LRCs via good polynomials

DOI10.1016/j.ffa.2024.102362arXiv2208.11358OpenAlexW4391211648MaRDI QIDQ6150566

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Publication date: 6 March 2024

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.11358

zbMATH Keywords

polynomial evaluationlocally repairable codesdistributed storage systemsgood polynomialssingleton-type bound

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Other types of codes (94B60)

Cites Work

• Optimal RS-like LRC codes of arbitrary length
• The Magma algebra system. I: The user language
• Good polynomials for optimal LRC of low locality
• The group structures of automorphism groups of elliptic curves over finite fields and their applications to optimal locally repairable codes
• A function field approach toward good polynomials for further results on optimal LRC codes
• Constructions of optimal locally recoverable codes via Dickson polynomials
• Optimal selection for good polynomials of degree up to five
• A Family of Optimal Locally Recoverable Codes
• On the Locality of Codeword Symbols
• Constructions of Optimal Cyclic $({r},{\delta })$ Locally Repairable Codes
• Optimal Locally Repairable Codes Via Elliptic Curves
• Optimal Binary Linear Locally Repairable Codes with Disjoint Repair Groups
• Constructions of Locally Recoverable Codes Which are Optimal
• Construction of Optimal Locally Repairable Codes via Automorphism Groups of Rational Function Fields
• Explicit Construction of Optimal Locally Recoverable Codes of Distance 5 and 6 via Binary Constant Weight Codes

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