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.
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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.
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Clone the repository:
git clone https://github.com/guptalab/GrayVT.git
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Enter into project repository:
cd GrayVT -
Navigate to the project directory:
cd Helberg Code/Theorem python main.py
- 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.
- 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.