Finite Field Sample Clauses

Finite Field. A finite field consists of a finite set of elements together with two binary operations called addition and multiplication, which satisfy certain arithmetic properties. The order of a finite field is the number of elements in the field. There exists a finite field of order q if and only if q is a prime power. If q is a prime power, then there is essentially only one finite field of order q; this field is denoted by Fq. There are, however, many ways of representing the elements of Fq. Some representations may lead to more efficient implementations of the field arithmetic in hardware or in software. If q=pm where p is a prime and m is a positive integer, then p is called the characteristic of Fq and m is called the extension degree of Fq.. More details about the prime field and finite field can be found in [11].
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