Project Overview: Loop Transversal Code

As part of my Master’s thesis, I developed the “Loop Transversal Code” project, which provides tools for constructing and analyzing syndrome maps in greedy loop transversal codes.

Online Demo

An interactive web-based version of the tool is available. Use it to explore syndrome mappings and parity check matrices directly in your browser:

👉 Loop Transversal Code Explorer

Project Overview

Traditional error-correcting codes are designed first, then analyzed to determine which errors they can correct. In contrast, the Loop Transversal Code method starts with a list of errors you want to fix and uses a greedy algorithm to build a custom code tailored to that list. This project demonstrates the greedy construction process and provides CLI tools for exploring syndrome mappings and parity check matrices.

Reference

This project is based on my Master’s thesis, which can be found here:

• Loop Transversal Code (NCKU Thesis Library)

Main Features

The command-line interface supports several key features:

• full-syndrome-mapping: Display syndrome mappings for all error patterns.
• basis-mapping: Display syndrome mappings for basis vectors.
• parity-check-matrix: Output the parity check matrix.
• all-mapping: Run all three features in sequence.

Installation

To run the project locally, install the required dependencies:

pip install -r requirements.txt

Example Usage

Here are a few examples of how to use the CLI:

# Example 1: Simple basis
python main.py all-mapping --error-patterns "[[1,0,0],[0,1,0],[0,0,1]]"

# Example 2: Custom error patterns
python main.py all-mapping --error-patterns "[[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,0,1,1],[0,0,0,1,0,0],[0,0,0,1,1,0],[0,0,1,0,0,0],[0,0,1,1,0,0],[0,1,0,0,0,0],[0,1,1,0,0,0],[1,0,0,0,0,0],[1,1,0,0,0,0]]"

# Example 3: Standard basis
python main.py parity-check-matrix --standard-basis 3

Testing

To run all tests and verify the core logic, use pytest:

pytest