Finite Field

What Does Finite Field Mean?

In mathematics, a finite field is a field that contains a finite number of elements. In other words, a finite field is a finite set on which the four basic operations – addition, subtraction, multiplication and division (excluding division by zero) – are defined and satisfy the field axioms/rules of the arithmetic. Finite fields are an important area of mathematics and computer science and are widely used in geometry, finite geometry, algebraic geometry, number theory, coding theory and cryptography.

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A finite field is also known as Galois field.

Techopedia Explains Finite Field

Any finite field must have a characteristic which is not zero, since containing a characteristic which is zero would lead it to be infinite. In a finite field, the number of elements is known as its order. The order of any finite field needs to be the power of a prime. In other words, Any finite field has pk elements where p is a prime and k a positive integer. In a finite field, a field comprised of no proper sub-fields is known as a prime field. All fields of a given order are isomorphic.

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Margaret Rouse

Margaret is an award-winning technical writer and teacher known for her ability to explain complex technical subjects to a non-technical business audience. Over the past twenty years, her IT definitions have been published by Que in an encyclopedia of technology terms and cited in articles by the New York Times, Time Magazine, USA Today, ZDNet, PC Magazine, and Discovery Magazine. She joined Techopedia in 2011. Margaret's idea of a fun day is helping IT and business professionals learn to speak each other’s highly specialized languages.