A Locally Recoverable Code is a code such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. When we have δ non-overlapping subsets of cardinality ri that can be used to recover the missing coordinate we say that a linear code C with length n, dimension k, minimum distance d has (r1,⋯, rδ) -locality and denote by [n, k, d; r1, r2, ⋯, rδ]. In this paper we provide a new upper bound for the minimum distance of these codes. Working with a finite number of subgroups of cardinality ri+1 of the automorphism group of a function field F| Fq of genus g ≥ 1 we propose a construction of [n, k, d; r1, r2, ⋯, rδ] -codes and apply the results to some well known families of function fields.

Locally Recoverable Codes from Automorphism Group of Function Fields of Genus g ≥ 1

Bartoli D.;
2020

Abstract

A Locally Recoverable Code is a code such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. When we have δ non-overlapping subsets of cardinality ri that can be used to recover the missing coordinate we say that a linear code C with length n, dimension k, minimum distance d has (r1,⋯, rδ) -locality and denote by [n, k, d; r1, r2, ⋯, rδ]. In this paper we provide a new upper bound for the minimum distance of these codes. Working with a finite number of subgroups of cardinality ri+1 of the automorphism group of a function field F| Fq of genus g ≥ 1 we propose a construction of [n, k, d; r1, r2, ⋯, rδ] -codes and apply the results to some well known families of function fields.
2020
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1481867
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