Decoding Algebraic Geometry codes by a key equation
Algebraic Geometry
2025-10-20 v1 Information Theory
Numerical Analysis
math.IT
Numerical Analysis
Abstract
A new effective decoding algorithm is presented for arbitrary algebraic-geometric codes on the basis of solving a generalized key equation with the majority coset scheme of Duursma. It is an improvement of Ehrhard's algorithm, since the method corrects up to the half of the Goppa distance with complexity order O(n**2.81), and with no further assumption on the degree of the divisor G.
Keywords
Cite
@article{arxiv.math/9910151,
title = {Decoding Algebraic Geometry codes by a key equation},
author = {J. I. Farran},
journal= {arXiv preprint arXiv:math/9910151},
year = {2025}
}
Comments
11 pages, submitted to "Finite Fields and their Applications"