Finding the minimum distance and decoding linear codes with Gaussian Elimination Method

03/13/2023
by   Tianshuo Yang, et al.
0

We propose an algorithm using the Gaussian elimination method to find the minimal Hamming distance and decode received messages of linear codes. This algorithm is easy to implement as it requires no Gröbner bases to compute solutions for systems of polynomial equations

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/09/2018

A decoding algorithm for binary linear codes using Groebner bases

It has been discovered that linear codes may be described by binomial id...
research
10/25/2019

Peterson-Gorenstein-Zierler algorithm for differential convolutional codes

Differential Convolutional Codes with designed Hamming distance are defi...
research
02/01/2021

Distance Enumerators for Number-Theoretic Codes

The number-theoretic codes are a class of codes defined by single or mul...
research
08/29/2018

Decoding binary Reed-Muller codes via Groebner bases

The binary Reed-Muller codes can be characterized as the radical powers ...
research
07/14/2020

Coding theory package for Macaulay2

In this Macaulay2 <cit.> package we define an object called linear code....
research
10/12/2018

Computing Elimination Ideals and Discriminants of Likelihood Equations

We develop a probabilistic algorithm for computing elimination ideals of...
research
05/22/2022

Average-case analysis of the Gaussian Elimination with Partial Pivoting

The Gaussian Elimination with Partial Pivoting (GEPP) is a classical alg...

Please sign up or login with your details

Forgot password? Click here to reset