https://github.com/lliepjiok/polynomial

Operations with polynomials over the finite field
https://github.com/lliepjiok/polynomial

field golang polynomial

Last synced: about 1 month ago
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Operations with polynomials over the finite field

• Host: GitHub
• URL: https://github.com/lliepjiok/polynomial
• Owner: LLIEPJIOK
• Created: 2024-11-25T17:12:16.000Z (about 2 months ago)
• Default Branch: master
• Last Pushed: 2024-11-25T17:29:48.000Z (about 2 months ago)
• Last Synced: 2024-11-25T18:30:48.570Z (about 2 months ago)
• Topics: field, golang, polynomial
• Language: Go
• Homepage:
• Size: 6.84 KB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
## Polynomial project

This program implements various operations with polynomials over the finite field $F_{2^n}$. It supports:

- **Addition**: Fast XOR operation between the coefficients of two polynomials.

- **Multiplication**: Polynomial multiplication with reduction modulo a given irreducible polynomial.

- **Division**: Computes the quotient and remainder of polynomial division.

- **Exponentiation**: Raises a polynomial to a specified power with modular reduction.

- **Inverse Polynomial**: Finds the multiplicative inverse using the extended Euclidean algorithm.

- **Irreducibility Check**: Verifies if a polynomial is irreducible over $F_{2^n}$.

This program is useful for applications in cryptography, error-correcting codes, and finite field algebra.

---

## Run

1.  Clone the repository:

    ```bash

    git clone [email protected]:LLIEPJIOK/polynomial.git

    ```

2.  Navigate to the project folder:

	```bash

	cd polynomial

	```

3.  Run the program:

    ```bash

    go run cmd/polynomial/main.go

    ```