The Asymptotic Theory of Algebraic-Geometry Codes

被引：0
|
作者：
Niederreiter, Harald [1 ]
机构：
[1] Austrian Acad Sci, RICAM, A-4040 Linz, Austria
来源：
FINITE FIELDS: THEORY AND APPLICATIONS | 2010年 / 518卷
关键词：
Error-correcting codes; Gilbert-Varshamov bound; TVZ bound; global function fields; algebraic-geometry codes; FUNCTION-FIELDS; NONLINEAR CODES; CURVES; IMPROVEMENTS; POINTS; BOUNDS; TOWER;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is well known that the asymptotic Gilbert-Varshamov bound in coding theory was improved in 1982 by the TVZ bound with the help of algebraic-geometry codes. In recent years, the TVZ bound was improved by using constructions of new types of algebraic-geometry codes. The paper surveys these recent developments and also provides a general introduction to the asymptotic theory of codes.
引用
收藏
页码：339 / 348
页数：10
相关论文
共 50 条
  • [41] On the unique representation of very strong algebraic geometry codes
    Irene Márquez-Corbella
    Edgar Martínez-Moro
    Ruud Pellikaan
    Designs, Codes and Cryptography, 2014, 70 : 215 - 230
  • [42] Evolving Secret Sharing Schemes Based on Polynomial Evaluations and Algebraic Geometry Codes
    Xing, Chaoping
    Yuan, Chen
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2024, 70 (05) : 3718 - 3728
  • [43] Erasure List-Decodable Codes From Random and Algebraic Geometry Codes
    Ding, Yang
    Jin, Lingfei
    Xing, Chaoping
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2014, 60 (07) : 3889 - 3894
  • [44] Improvements On Codes in Non Binary Fields Using Generalised Algebraic Geometry Codes
    Jibril, Mubarak
    Tomlinson, Martin
    Ahmed, Mohammed Zaki
    Tjhai, Cen
    2010 IEEE INTERNATIONAL CONFERENCE ON WIRELESS COMMUNICATIONS, NETWORKING AND INFORMATION SECURITY (WCNIS), VOL 2, 2010, : 202 - 205
  • [45] Applications of Pluripotential Theory to Algebraic Geometry
    Demailly, Jean-Pierre
    PLURIPOTENTIAL THEORY, CETRARO, ITALY 2011, 2013, 2075 : 143 - 263
  • [46] On improved asymptotic bounds for codes from global function fields
    Yang, Siman
    Qi, Lulu
    DESIGNS CODES AND CRYPTOGRAPHY, 2009, 53 (01) : 33 - 43
  • [47] Cryptanalysis of McEliece Cryptosystem Based on Algebraic Geometry Codes and Their Subcodes
    Couvreur, Alain
    Marquez-Corbella, Irene
    Pellikaan, Ruud
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2017, 63 (08) : 5404 - 5418
  • [48] Communication Efficient and Strongly Secure Secret Sharing Schemes Based on Algebraic Geometry Codes
    Martinez-Penas, Umberto
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2018, 64 (06) : 4191 - 4206
  • [49] Euclidean and Hermitian Self-Orthogonal Algebraic Geometry Codes and Their Application to Quantum Codes
    Jin, Lingfei
    Xing, Chaoping
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2012, 58 (08) : 5484 - 5489
  • [50] Quantum error-correcting codes from algebraic geometry codes of Castle type
    Carlos Munuera
    Wanderson Tenório
    Fernando Torres
    Quantum Information Processing, 2016, 15 : 4071 - 4088
12345