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Check whether polynomial over a Galois field is primitive
ck = gfprimck(a,p)
Note This function performs computations in GF(pm) where p is odd. To work in GF(2m), use the isprimitive function. For details, see Finding Primitive Polynomials. |
ck = gfprimck(a,p) returns a flag ck that indicates whether a polynomial over GF(p) is irreducible or primitive. a is a row vector that gives the coefficients of the polynomial in order of ascending powers. Each coefficient is between 0 and p-1. If m is the degree of the polynomial, then the output ck is
-1 if a is not an irreducible polynomial
0 if a is irreducible but not a primitive polynomial for GF(pm)
1 if a is a primitive polynomial for GF(pm)
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.
An irreducible polynomial over GF(p) of degree at least 2 is primitive if and only if it does not divide -1 + xk for any positive integer k smaller than pm-1.
gfprimfd, gfprimdf, gftuple, gfminpol, gfadd, Galois Fields of Odd Characteristic
[1] Clark, George C. Jr., and J. Bibb Cain, Error-Correction Coding for Digital Communications, New York, Plenum, 1981.
[1] Krogsgaard, K. and Karp, T., Fast Identification of Primitive Polynomials over Galois Fields: Results from a Course Project, ICASSP 2005, Philadelphia, PA, 2004.
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