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Algebraic Geometry Codes With Complementary Duals Exceed the Asymptotic Gilbert-Varshamov Bound.
- 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]
- Subjects :
- ALGEBRAIC geometry
FINITE fields
CRYPTOGRAPHY
ELLIPTIC curves
HERMITIAN structures
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 64
- Issue :
- 9
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 131346483
- Full Text :
- https://doi.org/10.1109/TIT.2017.2773057