This chapter excerpted from Hardware Implementation of Finite-Field Arithmetic describes several algorithms, namely, the integer division, the reduction mod B k — a, the precomputation of B ik mod m, ...

Combinatorial geometry and finite fields constitute a vibrant area of research that bridges classical geometric intuition with discrete algebraic structures. This interdisciplinary field examines the ...

Our research group is concerned with two lines of investigation: the construction and study of (new) cohomology theories for algebraic varieties and the study of various aspects of the Langlands ...

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 ...

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 ...