Constructions of Locally Recoverable Codes Which are Optimal

DOI10.1109/TIT.2019.2939464zbMath1433.94129arXiv1806.11492MaRDI QIDQ5211590

Giacomo Micheli

Publication date: 28 January 2020

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.11492

Mathematics Subject Classification ID

Linear codes (general theory) (94B05)

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A function field approach toward good polynomials for further results on optimal LRC codes ⋮ On construction and (non)existence of \(c\)-(almost) perfect nonlinear functions ⋮ Investigating the exceptionality of scattered polynomials ⋮ Optimal selection for good polynomials of degree up to five ⋮ A characterization of optimal locally repairable codes ⋮ Algebraic constructions of complete \(m\)-arcs ⋮ The minimum locality of linear codes ⋮ New upper bounds and constructions of multi-erasure locally recoverable codes ⋮ New constructions of optimal \((r, \delta)\)-LRCs via good polynomials ⋮ Constructions of optimal locally recoverable codes via Dickson polynomials ⋮ Exceptional scatteredness in prime degree ⋮ Good polynomials for optimal LRC of low locality ⋮ Optimal RS-like LRC codes of arbitrary length

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