Check whether polynomial over Galois field is primitive
ck = gfprimck(a)
ck = gfprimck(a,p)
Note:
This function performs computations in GF(p^{m}),
where p is prime. If you are working in GF(2^{m}),
use the |
ck = gfprimck(a)
checks
whether the degree-m GF(2) polynomial a
is a primitive
polynomial for GF(2^{m}), where m = length(a
)
- 1. The output ck
is as follows:
-1 if a
is not an irreducible polynomial
0 if a
is irreducible but not a
primitive polynomial for GF(p
^{m})
1 if a
is a primitive polynomial
for GF(p
^{m})
ck = gfprimck(a,p)
checks
whether the degree-m GF(P) polynomial a
is a primitive
polynomial for GF(p^{m}). p is a prime number.
a
is either a polynomial string or
a row vector representing the polynomial by listing its coefficients
in ascending order. For example, in GF(5), '4 + 3x + 2x^3'
and [4
3 0 2]
are equivalent.
This function considers the zero polynomial to be "not irreducible" and considers all polynomials of degree zero or one to be primitive.
Characterization of Polynomials contains examples.
[1] Clark, George C. Jr., and J. Bibb Cain, Error-Correction Coding for Digital Communications, New York, Plenum, 1981.
[2] Krogsgaard, K., and T., Karp, Fast Identification of Primitive Polynomials over Galois Fields: Results from a Course Project, ICASSP 2005, Philadelphia, PA, 2004.