Find minimal polynomial of Galois field element
pol = gfminpol(k,m)
pol = gfminpol(k,m,p)
pol = gfminpol(k,prim_poly,p)
Note:
This function performs computations in GF(p^{m}),
where p is prime. To work in GF(2^{m}), use
the |
pol = gfminpol(k,m)
produces
a minimal polynomial for each entry in k
. k
must
be either a scalar or a column vector. Each entry in k
represents
an element of GF(2^{m}) in exponential format.
That is, k
represents alpha^k
,
where alpha is a primitive element in GF(2^{m}).
The ith row of pol
represents
the minimal polynomial of k
(i).
The coefficients of the minimal polynomial are in the base field
GF(2) and listed in order of ascending exponents.
pol = gfminpol(k,m,p)
finds
the minimal polynomial of A^{k} over GF(p
),
where p
is a prime number, m
is
an integer greater than 1, and A is a root of the default primitive
polynomial for GF(p^m
). The format of the output
is as follows:
If k
is a nonnegative integer, pol
is
a row vector that gives the coefficients of the minimal polynomial
in order of ascending powers.
If k
is a vector of length len all
of whose entries are nonnegative integers, pol
is
a matrix having len rows; the rth row of pol
gives
the coefficients of the minimal polynomial of A^{k(r)} in
order of ascending powers.
pol = gfminpol(k,prim_poly,p)
is
the same as the first syntax listed, except that A is a root of the
primitive polynomial for GF(p
^{m})
specified by prim_poly
. prim_poly
is
a row vector that gives the coefficients of the degree-m primitive
polynomial in order of ascending powers.
The syntax gfminpol(k,m,p)
is used in the
sample code in Characterization of Polynomials.