This project implements polynomial arithmetic in Galois Fields (GF(2^m)) with a focus on mathematical rigor, computational accuracy, and user-centered design. It provides a robust backend and an ...

Abstract: This paper presents a very large-scale integration implementation of Galois field arithmetic for high-speed error-control coding applications that is based on the field GF(p/sup m/) with m a ...

This project implements the Shamir Secret Sharing algorithm in Java, demonstrating both standard polynomial interpolation and Galois Field arithmetic. It visualizes the shares generated using the ...

Formal verification of arithmetic circuits is a rigorous approach that employs mathematical techniques to ascertain the correctness of hardware designs implementing arithmetic operations. This ...

Arithmetic dynamics investigates the behaviour of iterated functions—often polynomials or rational maps—over number fields and function fields, while Galois theory provides the framework to analyse ...

means that the level of factor F is computed by adding the levels of B and D and two times the levels of C and E, all modulo 3. Note that if q is not a prime number, Galois field arithmetic is not ...

The FACTEX procedure constructs a fractional design for q-level factors using the Galois field (or finite field) of size q. This is a system with q elements and two operations + and ×, which satisfy ...

Finite fields, also known as Galois fields, are algebraic structures that have a finite number of elements and follow specific mathematical rules. They play a fundamental role in various areas of ...