CodingTheoryUtils.jl

CodingTheoryUtils.jl is a Julia package that provides utilities for coding theory, with a particular focus on Galois field operations and related mathematical tools. This package is designed to support research and development in coding theory, error correction, and related fields.

Features

• Galois Field Operations

  • Field size and extension degree calculations
  • Primitive root operations
  • Trace function implementation
  • Minimum polynomial computation
  • Conjugate element calculations
  • Root finding in finite fields

• Polynomial Operations

  • Polynomial representation and manipulation
  • Conversion between different polynomial formats
  • Companion matrix generation
  • Polynomial evaluation and factorization

• Utility Functions

  • Binary-decimal conversions
  • Vector operations
  • Matrix transformations
  • Pretty printing for Galois field elements
  • One-hot vector generation

Installation

To install the package, use the Julia package manager:

using Pkg
Pkg.add("CodingTheoryUtils")

Usage

Here's a simple example of using the package:

using CodingTheoryUtils

# Create a Galois field element
x = F2(1)

# Calculate field size
size = field_size(x)

# Find primitive root
root = primitive_root(F2)

# Convert between different representations
binary = de2bi(5)
decimal = bi2de(binary)

Documentation

Documentation is currently under construction. Please check back later for detailed documentation.

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

License

This project is licensed under the GNU General Public License Version 3 - see the LICENSE file for details.