Nonlinear codes from points of bounded height

被引：1

作者：

Hurlburt, Chris ^{[1
]}

Thunder, Jeffrey Lin ^{[1
]}

机构：

[1] No Illinois Univ, Dept Math, De Kalb, IL 60115 USA

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2007年 / 13卷 / 02期

基金：

美国国家科学基金会;

关键词：

nonlinear error correcting codes; algebraic-geometric codes;

D O I：

10.1016/j.ffa.2005.11.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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, 200 1, 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, 200 1, 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. (c) 2005 Published by Elsevier Inc.

引用

页码：281 / 292

页数：12