Optimal Locally Repairable Codes Via Elliptic Curves

DOI10.1109/TIT.2018.2844216zbMath1431.94207arXiv1712.03744OpenAlexW2963503165WikidataQ129721007 ScholiaQ129721007MaRDI QIDQ4611419

Xing, Chaoping, Xudong Li, Liming Ma

Publication date: 18 January 2019

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

Full work available at URL: https://arxiv.org/abs/1712.03744

zbMATH Keywords

elliptic curvesfamily of q-ary optimal locally repairable codes

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Elliptic curves (14H52) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (15)

Toward good families of codes from towers of surfaces ⋮ Application of optimal \(p\)-ary linear codes to alphabet-optimal locally repairable codes ⋮ Optimal cyclic locally repairable codes with unbounded length from their zeros ⋮ A characterization of optimal locally repairable codes ⋮ New upper bounds and constructions of multi-erasure locally recoverable codes ⋮ Singleton-optimal LRCs and perfect LRCs via cyclic and constacyclic codes ⋮ New constructions of optimal \((r, \delta)\)-LRCs via good polynomials ⋮ Codes with locality from cyclic extensions of Deligne-Lusztig curves ⋮ A characterization of optimal constacyclic locally repairable codes ⋮ Perfect LRCs and \(k\)-optimal LRCs ⋮ Good polynomials for optimal LRC of low locality ⋮ Optimal cyclic \((r, \delta )\) locally repairable codes with unbounded length ⋮ The group structures of automorphism groups of elliptic curves over finite fields and their applications to optimal locally repairable codes ⋮ Codes for Distributed Storage ⋮ Codes in the Sum-Rank Metric: Fundamentals and Applications

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