Description
Evaluation AG code on algebraic curves built from a Galois cover \(\phi:Y\to X\), where the recovery sets are fibres over rational points of \(X\) that split completely in the cover [3; Def. 15.9.10][3; Thm. 15.9.14]. This generalizes the Tamo-Barg construction from \(PG(1,q)\) to longer AG codes, and variants can be built with higher local distance or availability \(2\) via fibre products of curves [3; Thm. 15.9.19][3; Thm. 15.9.21].Rate
Tamo-Barg-Vladut codes on asymptotically maximal curves improve upon the asymptotic LRC GV bound [2].Cousins
- Availability code— Fibre-product constructions of Tamo-Barg-Vladut codes yield LRCs with availability \(2\) [3; Thm. 15.9.21].
- Hermitian code— Hermitian-curve examples of these codes are given in [3; Rem. 15.9.16].
Primary Hierarchy
Parents
Tamo-Barg-Vladut codes are evaluation AG codes on algebraic curves built from curve covers [3; Thm. 15.9.14].
Tamo-Barg-Vladut codes form a family of locally recoverable codes obtained from algebraic curves [3; Thm. 15.9.14].
Tamo-Barg-Vladut code
Children
Tamo-Barg codes are the \(PG(1,q)\)/genus-zero instance of the covering-based construction that later yields Tamo-Barg-Vladut codes [3; Sec. 15.9.4].
References
- [1]
- A. Barg, I. Tamo, and S. Vladut, “Locally recoverable codes on algebraic curves”, (2015) arXiv:1501.04904
- [2]
- A. Barg, I. Tamo, and S. Vlăduţ, “Locally recoverable codes on algebraic curves”, 2015 IEEE International Symposium on Information Theory (ISIT) 1252 (2015) arXiv:1603.08876 DOI
- [3]
- A. Couvreur, H. Randriambololona, “Algebraic Geometry Codes and Some Applications.” Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
Page edit log
- Victor V. Albert (2024-01-11) — most recent
Cite as:
“Tamo-Barg-Vladut code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/tamo_barg_vladut