Communications Toolbox    
gfprimck

Check whether a polynomial over a Galois field is primitive

Syntax

Description

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

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

Examples

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 + xk for any positive integer k smaller than pm-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, 1981.


  gfpretty gfprimdf