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Syndrome Generation and Error Location Search for the Decoding of Algebraic-Geometry Codes on Plane Garcia–Stichtenoth Curves.
- Source :
- IEEE Transactions on Information Theory; Dec2014, Vol. 60 Issue 12, p7464-7472, 9p
- Publication Year :
- 2014
-
Abstract
- In this paper, the basic function field of an asymptotically optimal tower of function fields by Garcia and Stichtenoth is studied, where bases of one-point linear systems can be explicitly constructed. A representation of finite GF(q^2) -rational points on the associated plane curve is derived in this paper. This representation is exploited to extend the use of Horner’s loops and the mechanism of Chien search in the decoding of Reed–Solomon codes for syndrome generation and error-location search, respectively, to algebraic-geometry codes built on the plane Garcia–Stichtenoth curve. [ABSTRACT FROM AUTHOR]
- Subjects :
- ERROR-correcting codes
ALGEBRAIC geometric codes
CURVES
POLYNOMIALS
LINEAR systems
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 60
- Issue :
- 12
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 100027665
- Full Text :
- https://doi.org/10.1109/TIT.2014.2361794