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Nonlinear codes from points of bounded height
- Source :
-
Finite Fields & Their Applications . Apr2007, Vol. 13 Issue 2, p281-292. 12p. - Publication Year :
- 2007
-
Abstract
- Abstract: This paper generalizes Elkies'' construction of error-correcting nonlinear codes found in [N. Elkies, Excellent nonlinear codes from modular curves, in: Proceedings of the 33rd Annual ACM Symposium on the Theory of Computing, STOC''01, Hersonissos, Crete, Greece, 2001, pp. 200–208]. The generalization produces a precise average code size over codes in the new construction. The result is a larger family of codes with similar transmission rates and error detection rates to the nonlinear codes found in [N. Elkies, Excellent nonlinear codes from modular curves, in: Proceedings of the 33rd Annual ACM Symposium on the Theory of Computing, STOC''01, Hersonissos, Crete, Greece, 2001, pp. 200–208]. Moreover, we exhibit a connection between these nonlinear codes and solutions to simple homogeneous linear equations defined over the function field of a curve. [Copyright &y& Elsevier]
- Subjects :
- *CURVES
*EQUATIONS
*CALCULUS
Subjects
Details
- Language :
- English
- ISSN :
- 10715797
- Volume :
- 13
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Finite Fields & Their Applications
- Publication Type :
- Academic Journal
- Accession number :
- 24221183
- Full Text :
- https://doi.org/10.1016/j.ffa.2005.11.001