Permutation decoding of algebraic geometry codes from Hermitian and norm-trace curves

TL;DR

This paper explores permutation decoding techniques for algebraic geometry codes derived from Hermitian and norm-trace curves, focusing on automorphisms to correct burst errors in received messages.

Contribution

It introduces permutation decoding sets based on curve automorphisms for specific algebraic geometry codes, enhancing error correction capabilities.

Findings

Permutation decoding sets are constructed for codes on Hermitian and norm-trace curves.

These sets effectively correct burst errors in the specified algebraic geometry codes.

The approach leverages automorphisms of the underlying algebraic curves.

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.