Locally recoverable codes from algebraic curves and surfaces

Abstract

A locally recoverable code is a code over a finite alphabet such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. Building on work of Barg, Tamo, and Vlăduţ, we present several constructions of locally recoverable codes from algebraic curves and surfaces.

27 pages

References in corpus (4)

• A family of optimal locally recoverable codes
• Cyclic LRC Codes, binary LRC codes, and upper bounds on the distance of cyclic codes
• Combinatorial Alphabet-Dependent Bounds for Locally Recoverable Codes
• Locally Recoverable Codes with Availability $t\ge 2$ from Fiber Products of Curves

Cited by in corpus (12)

• Construction of optimal locally recoverable codes and connection with hypergraph
• Explicit optimal-length locally repairable codes of distance 5
• Algebraic geometry codes and some applications
• Optimal $(r,\delta )$-LRCs from monomial-Cartesian codes and their subfield-subcodes
• Locally Recoverable Codes with Availability $t\ge 2$ from Fiber Products of Curves
• Bandwidth Cost of Code Conversions in Distributed Storage: Fundamental Limits and Optimal Constructions
• Cyclic and convolutional codes with locality
• Repeated-root Constacyclic Codes with Optimal Locality
• Locally Recoverable Codes with availability from a family of fibered surfaces
• The group structures of automorphism groups of elliptic function fields over finite fields and their applications to optimal locally repairable codes
• Convertible Codes: Efficient Conversion of Coded Data in Distributed Storage
• Mathematical LoRE: Local Recovery of Erasures using Polynomials, Curves, Surfaces, and Liftings