Reed-Solomon Error Correcting Code Implementation

Introduction

This project is part of the course SM404 - Computational Introduction to Number Theory. It implements the Integer version of the Reed-Solomon Error Correcting code.

Functionality

The implemented code performs the following tasks:

1. Setup global parameters for the Reed-Solomon code.
2. Generate primes and setup parameters for the code.
3. Encode a message using the Reed-Solomon code for transmission.
4. Simulate transmission with corruption.
5. Decode the received message using the Reed-Solomon code.

Functions Implemented

1. Extended Euclid's Greatest Common Divisor Algorithm
2. Binary version of Euclid's Greatest Common Divisor Algorithm
3. Chineese Remainder Theorem
4. Miller Rabin Primality Test
5. Binary Exponentiation
6. Modular Inverse

Usage

1. Ensure you have Python installed on your system.
2. Install the required library gmpy2 using pip install gmpy2.
3. Run the Python script Number_Theory.py.
4. Enter the message, message bound, and corruption fraction as prompted.
5. The script will output the decoded message if successful, otherwise, it will return an error.

Files

• Number_Theory.py: Main Python script implementing the Reed-Solomon code.
• README.md: This readme file providing information about the project.
• (You can list any other relevant files here)

Acknowledgements

• The assignment details and requirements are based on the course SM404 and the textbook by V. Shoup.
• The code implementation is based on algorithms and concepts discussed in the textbook.

Contributors

• Sarvesh Kumar . A
• Ayush Gupta