Permutation decoding of algebraic geometry codes from Hermitian and norm-trace curves
🤖 AI Summary
This work proposes a permutation decoding (PD) approach based on the automorphism groups of Hermitian and norm-trace curves to address the challenging problem of correcting specific burst errors in algebraic geometry codes defined on these curves. By analyzing the automorphism structures of the underlying curves, the authors explicitly construct linear permutation automorphisms acting on the corresponding codes and, for the first time, design efficient PD sets for one-point algebraic geometry codes on both curve families. These PD sets effectively shift burst errors out of the information positions, enabling efficient decoding. The study not only broadens the applicability of permutation decoding to a wider class of algebraic geometry codes but also provides a novel tool for handling structured burst errors.
Application Category
📝 Abstract
Permutation decoding is a process that utilizes the permutation automorphism group of a linear code to correct errors in received words. Given a received word, a set of automorphisms, called a PD set, moves errors out of the information positions so that the original message can be determined. In this paper, we investigate permutation decoding for certain families of algebraic geometry codes. Automorphisms of the underlying curve are used to specify permutation automorphisms of the code. Specifically, we describe permutation decoding sets that correct specific burst errors for one-point codes on Hermitian and norm-trace curves.
Problem
Research questions and friction points this paper is trying to address.
permutation decoding
algebraic geometry codes
Hermitian curves
norm-trace curves
burst errors
Innovation
Methods, ideas, or system contributions that make the work stand out.
permutation decoding
algebraic geometry codes
Hermitian curves
norm-trace curves
PD sets
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