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Algebraic Geometry Codes With Complementary Duals Exceed the Asymptotic Gilbert-Varshamov Bound.

Authors :
Jin, Lingfei
Xing, Chaoping
Source :
IEEE Transactions on Information Theory. Sep2018, Vol. 64 Issue 9, p6277-6282. 6p.
Publication Year :
2018

Abstract

It was shown by Massey that linear complementary dual (LCD) codes are asymptotically good. In 2004, Sendrier proved that LCD codes meet the asymptotic Gilbert–Varshamov (GV) bound. Until now, the GV bound still remains to be the best asymptotical lower bound for LCD codes. In this paper, we show that an algebraic geometry code over a finite field of even characteristic is equivalent to an LCD code and consequently there exists a family of LCD codes that are equivalent to algebraic geometry codes and exceed the asymptotical GV bound. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00189448
Volume :
64
Issue :
9
Database :
Academic Search Index
Journal :
IEEE Transactions on Information Theory
Publication Type :
Academic Journal
Accession number :
131346483
Full Text :
https://doi.org/10.1109/TIT.2017.2773057