# Galois field

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## Galois field

[′gal‚wä ‚fēld]
(mathematics)
A type of field extension obtained from considering the coefficients and roots of a given polynomial. Also known as root field; splitting field.
References in periodicals archive ?
We tested performance with the Galois Field of size 4, 8 and 16, and the results for each test conditions (GF=4/8/16) was examined.
In Section 2, we discuss the properties of the background Galois field GF([2.sup.8]).
It is also shown in  that the larger the Galois Field, the higher the probability of linear independence of its elements (coding coefficients) as concisely summarised in Table 1.
Then, p1 was generated using RS(10,8), and p2 using an RS(6,4) code specification in the Galois field GF([2.sup.4]).
Source messages [X.bar] = ([x.sub.1], ..., [x.sub.[omega]]) arranged in a row vector over a Galois field [F.sub.q] of size q are transmitted to the source 5 through [omega] imaginary channels in In (5).
[15.] Mastrovito, E, "VLSI Architectures for Computation in Galois Fields".
Although they are designed to be universal, Galois Field GF([257.sup.32]) was chosen for the implementation because of the ease of byte representation and therefore the possibility of faster implementation.
(1) When Galois field m = 8, the number of data source node sends each time: DataNum = 4, transmission radius of each node: radius = 3 x sqrt (scale) = 3 x 10 = 30, we test the relationship between decoding success probability and total node number NodeNum when three nodes are co-wiretapping.
This fuzzy set gives the grade of membership of each element of Galois field GF([2.sup.8]) in the secret image.
The latter is actually a composite function of an inversion over Galois Field (GF) with an affine mapping.
In one of our debut papers devoted to the theory of pencil-generated temporal dimensions, (1) we discussed basic properties of the structure of time over a Galois field of even order, GF([2.sup.n]).
NON-BINARY low-density parity-check (NB-LDPC) codes are a original kind of linear block codes defined over Galois fields (GFs) GF(q = 2p) with p > 1.

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