Find primitive polynomials for Galois field
pr = primpoly(m)
pr = primpoly(m,opt)
pr = primpoly(m...,'nodisplay')
pr = primpoly(m) returns the primitive
polynomial for GF(2^m), where m is an integer
between 2 and 16. The Command Window displays the
polynomial using "D" as an indeterminate quantity. The output
argument pr is an integer whose binary representation indicates the
coefficients of the polynomial.
pr = primpoly(m,
returns one or more primitive polynomials for GF(opt)2^m). The output
pol depends on the argument opt as
shown in the table below. Each element of the output argument pr is
an integer whose binary representation indicates the coefficients of the corresponding
polynomial. If no primitive polynomial satisfies the constraints, pr
is empty.
| opt | Meaning of pr |
|---|---|
'min' | One primitive polynomial for GF(2^m) having
the smallest possible number of nonzero terms |
'max' | One primitive polynomial for GF(2^m) having
the greatest possible number of nonzero terms |
'all' | All primitive polynomials for GF(2^m) |
| Positive integer k | All primitive polynomials for GF(2^m) that
have k nonzero terms |
pr = primpoly(m...,'nodisplay') prevents the
function from displaying the result as polynomials in "D" in the
Command Window. The output argument pr is unaffected by the
'nodisplay' option.
The first example below illustrates the formats that primpoly uses
in the Command Window and in the output argument pr. The subsequent
examples illustrate the display options and the use of the
opt argument.
pr = primpoly(4) pr1 = primpoly(5,'max','nodisplay') pr2 = primpoly(5,'min') pr3 = primpoly(5,2) pr4 = primpoly(5,3);
The output is below.
Primitive polynomial(s) =
D^4+D^1+1
pr =
19
pr1 =
61
Primitive polynomial(s) =
D^5+D^2+1
pr2 =
37
No primitive polynomial satisfies the given constraints.
pr3 =
[]
Primitive polynomial(s) = D^5+D^2+1 D^5+D^3+1