Naisargik and Inverse Naisargik Images in Error-Correcting Codes

Overview

This document outlines the mathematical properties and applications of Naisargik and inverse Naisargik images in error-correcting codes, specifically focusing on VT (Vertical Redundancy Check) codes and Helberg codes. These codes are utilized for single error correction (VT) and multiple error correction (Helberg) scenarios.

Description

• VT Codes: VT codes are proficient in single error correction. Naisargik images map quaternary ($Z_4$) VT codes to binary ($Z_2^2$) codes. The intersection of deletion spheres generated by two Naisargik images of VT codes implies identical weights.
• Helberg Codes: Helberg codes excel in multiple error correction. Naisargik images of quaternary Helberg codes can correct $s+1$ deletions, while inverse Naisargik images of binary Helberg codes correct $\lfloor\frac{s}{2}\rfloor$ errors.

Installation

1. Clone the repository:

   git clone https://github.com/guptalab/GrayVT.git

2. Enter into project repository:

   cd GrayVT

3. Navigate to the project directory:

   cd Helberg Code/Theorem
   python main.py

Usage

• Researchers and practitioners interested in error-correction coding theory can refer to this paper for mathematical proofs and insights into the properties of Naisargik and inverse Naisargik images.
• Implementers of error-correcting codes can utilize these findings to enhance the robustness and efficiency of their systems, particularly in scenarios requiring single or multiple error correction.

Contributors

• Kalp Pandya
• Devdeep Shetranjiwala
• Naisargi Savaliya
• Prof. Manish K. Gupta

Note: This README serves as a brief introduction to the concepts discussed. For comprehensive understanding and detailed proofs, please refer to the associated paper.