The group structures of automorphism groups of elliptic curves over finite fields and their applications to optimal locally repairable codes

DOI10.1016/j.jcta.2022.105686OpenAlexW4297977762MaRDI QIDQ2084990

Liming Ma, Xing, Chaoping

Publication date: 14 October 2022

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2022.105686

zbMATH Keywords

elliptic curvesrational pointsautomorphism groupslocally 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 (1)

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

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Optimal rate algebraic list decoding using narrow ray class fields
• A new family of maximal curves over a finite field
• On subfields of the Hermitian function field involving the involution automorphism
• Locally recoverable codes from algebraic curves and surfaces
• The complete list of genera of quotients of the \(\mathbb{F}_{q^2}\)-maximal Hermitian curve for \(q \equiv 1 \pmod 4\)
• Towards a characterization of subfields of the Deligne-Lusztig function fields
• Algebraic curves with many automorphisms
• On the locality of codeword symbols in non-linear codes
• Optimal Locally Repairable Codes and Connections to Matroid Theory
• Locally Repairable Codes
• A Family of Optimal Locally Recoverable Codes
• On the Locality of Codeword Symbols
• Algebraic Function Fields and Codes
• A Note on Elliptic Curves Over Finite Fields
• Optimal Locally Repairable Codes Via Elliptic Curves
• Optimal Locally Repairable Codes of Distance 3 and 4 via Cyclic Codes
• Subspace designs based on algebraic function fields
• On Optimal Locally Repairable Codes With Super-Linear Length
• Constructive Asymptotic Bounds of Locally Repairable Codes via Function Fields
• Construction of Asymptotically Good Locally Repairable Codes via Automorphism Groups of Function Fields
• Construction of Optimal Locally Repairable Codes via Automorphism Groups of Rational Function Fields
• The asymptotic behavior of automorphism groups of function fields over finite fields
• Locality and Availability of Array Codes Constructed From Subspaces
• Explicit Construction of Optimal Locally Recoverable Codes of Distance 5 and 6 via Binary Constant Weight Codes
• Locally Recoverable Codes on Algebraic Curves
• Abelian varieties over finite fields

This page was built for publication: The group structures of automorphism groups of elliptic curves over finite fields and their applications to optimal locally repairable codes