English

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"