Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0107102

Some Good Error-Correcting Codes from Algebraic-Geometric Codes

Hao Chen

Published Jul 20, 2001• 1 citation
arXivHTMLPDF

Abstract

Algebraic-geometric codes on Garcia-Stichtenoth family of curves are used to construct the asymptotically good quantum codes.
DOI
10.48550/arxiv.quant-ph/0107102

Related papers

Construction of Asymptotically Good p~m-ary Quantum Codes

Hao Chen

This paper applies algebraic-geometric codes to construct a family of asymptot- ically good p~m-ary quantum codes,for any prime power p~m.

Chinese Annals of Mathematics•Jan 1, 2008•0 citations

Asymptotically good quantum codes

Alexei Ashikhmin, Simon N. Litsyn, Michael Anatol'evich Tsfasman

Using algebraic geometry codes we give a polynomial construction of quantum codes with asymptotically non-zero rate and relative distance.

arXiv:quant-ph/0006061•Physical Review A•Feb 1, 2001•90 citations

Improvement of Ashikhmin-Litsyn-Tsfasman bound for quantum codes

R. Matsumoto

We improve performance of the asymptotically good quantum codes constructed by Ashikhmin, Litsyn, and Tsfasman (see Phys. Rev. A, vol.63, no.3, p.032311, Mar. 2001), by using more rational points on algebraic curves.

IEEE International Symposium on Information Theory (ISIT)•Jun 25, 2003•4 citations

Improvement of Ashikhmin-Litsyn-Tsfasman bound for quantum codes

Ryutaroh Matsumoto

We improve performance of the asymptotically good quantum codes constructed by Ashikhmin, Litsyn and Tsfasman (see Phys. Rev. A, vol.63, no.3, p.032311, 2001), by using more rational points on algebraic curves.

arXiv:quant-ph/0107129•IEEE Transactions on Information Theory•Jul 1, 2002•39 citations

Good and asymptotically good quantum codes derived from algebraic geometry

Giuliano G. La Guardia, Francisco Revson F. Pereira

Quantum Information Processing•May 13, 2017•20 citations

Quantum Algebraic-Geometric Codes

Chiu Fan Lee

This is a Part III essay aiming to discuss the contruction of quantum error-correcting codes through the use of the theory of algebraic function fields, which produces codes with asymptotically good parameters. This exposition emphasises constructibility and several applications of the main theorem (theorem 6.2) are given. Prerequisites are the first 12 lectures of the Part III course Quantum Information Theory [16] or chapter 7 of Preskill’s Lecture Notes [15], and the first two chapters of Stichtenoth’s Algebraic Function Fields and Codes [19].

•Jan 1, 2003•0 citations
This is a Part III essay aiming to discuss the contruction of quantum error-correcting codes through the use of the theory of algebraic function fields, which produces codes with asymptotically good parameters. This exposition emphasises constructibility and several applications of the main theorem (theorem 6.2) are given. Prerequisites are the first 12 lectures of the Part III course Quantum Information Theory [16] or chapter 7 of Preskill’s Lecture Notes [15], and the first two chapters of Stichtenoth’s Algebraic Function Fields and Codes [19].