primitive polynomial


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primitive polynomial

[′prim·əd·iv ‚päl·i′nō·mē·əl]
(mathematics)
A polynomial with integer coefficients which have 1 as their greatest common divisor.
References in periodicals archive ?
For each primitive polynomial, take p positive odd as initial value [m.
This shortness is compensated by simply changing the primitive polynomial of the generator.
The choice of a feedback polynomial is made between preliminarily calculated primitive polynomials in GF([p.
The positive integer m is the degree of a primitive polynomial (we discuss this below) used to generate the elements of the finite field.
Since m = 5, we need a primitive polynomial of degree 5.
Using this analogy we identify the primitive polynomial in the SRG as the object to parameterize.
The author chose p(x) to be a primitive polynomial of degree 19 drawn from Peterson [1961]:
i] in GF(m), is a primitive polynomial modulo m, which means that all powers of x modulo f(x) and modulo m contitute S*.
this test requires only the calculation of a binary matrix whose size is about p x p, where p is the degree of the primitive polynomial.
For an explanation of the CRC algorithms and their maximally generating primitive polynomial lists, trade-offs, and error-detection probability predictions, see [1] and [2].
The next phase of the research project is to develop an algorithm to generate primitive polynomials of degree higher than 256, in order to obtain pseudorandom sequences with longer period.
Our calculations also show that there are polynomials at distance four from the set of primitive polynomials.