Communications Toolbox

gfprimck

Check whether a polynomial over a Galois field is primitive

Syntax

ck = gfprimck(a);
ck = gfprimck(a,p);

Description

ck = gfprimck(a) returns a flag ck that indicates whether a polynomial over GF(2) is irreducible or primitive. a is a row vector that gives the coefficients of the polynomial in order of ascending powers. Each coefficient is either 0 or 1, since the field is GF(2). 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(2^m)
• 1 if a is a primitive polynomial for GF(2^m)

This function considers the zero polynomial to be "not irreducible" and considers all polynomials of degree zero or one to be primitive.

ck = gfprimck(a,p) is the same as the syntax listed above, except that 2 is replaced by a prime number p.

Examples

The section Characterization of Polynomials contains examples.

Algorithm

An irreducible polynomial over GF(p) of degree at least 2 is primitive if and only if it does not divide -1 + x^k for any positive integer k smaller than p^m-1.

See Also
gfprimfd, gfprimdf, gftuple, gfminpol, gfadd

References

Clark, George C. Jr. and J. Bibb Cain. Error-Correction Coding for Digital Communications. New York: Plenum Press, 1981.

gfpretty

gfprimdf