primitive polynomial

A 'primitive polynomial' plays a crucial role in algebra and field theory, especially in generating elements of finite fields and in applications like cryptography and coding theory.

πŸ‡ΊπŸ‡Έ US Voice:
πŸ‡¬πŸ‡§ UK Voice:

Definition

C2Field Theory

(technical, academic)A polynomial over a finite field whose roots generate all elements of the field.

Example

  • In finite field theory, a primitive polynomial is essential for generating all elements of the field.

C2Algebra

(technical, academic)A polynomial that cannot be factored into simpler polynomials and whose greatest common divisor of coefficients is one.

Example

  • A primitive polynomial in algebra ensures that the greatest common divisor of its coefficients is one.

C2Cryptography

(technical)An irreducible polynomial used in algorithms to generate sequences with desirable properties for secure communication.

Example

  • Primitive polynomials are used in cryptographic algorithms to ensure secure data transmission.

Similar

Terms that have similar or relatively close meanings to "primitive polynomial":

primitive elementminimal polynomialpolynomial basischaracteristic polynomialprime idealalmost primecyclic numberprimitive recursion