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gfprimdf

Provide default primitive polynomials for Galois field

Syntax

pol = gfprimdf(m)
pol = gfprimdf(m,p)

Description

Note

This function performs computations in GF(pm), where p is prime. To work in GF(2m), use the primpoly function. For details, see Finding Primitive Polynomials in Primitive Polynomials and Element Representations.

pol = gfprimdf(m) outputs the default primitive polynomial pol in GF(2m).

pol = gfprimdf(m,p) returns the row vector that gives the coefficients, in order of ascending powers, of the default primitive polynomial for GF(pm). m is a positive integer and p is a prime number.

Examples

The command below shows that 2 + x + x2 is the default primitive polynomial for GF(52).

pol = gfprimdf(2,5)
pol =

     2     1     1

The code below displays the default primitive polynomial for each of the fields GF(3m), where m ranges between 3 and 5.

for m = 3:5
   gfpretty(gfprimdf(m,3))
end

The output is below.

                                            3
                                 1 + 2 X + X 
 
                                           4
                                  2 + X + X 
 
                                            5
                                 1 + 2 X + X 

Introduced before R2006a