Due: Wednesday, April 16, 1998
be the primitive element of GF(26)
which is the zero of the primitive polynomial:
p(x) = x6 + x + 1 .
be the polynomial of smallest degree having the following zeros:
x, x2, x3,
Let V =
( g(x) ) be the corresponding cyclic code
of shortest length.
you have not installed the symbolic fonts on your web browser, then the
will look like x's.
(a) Write g(x)
as a product of minimal polynomials mi(x),
is the minimum polynomial of xi.
(Do not explicitly compute the mi(x)'s.)
(b) Find the degree
(c) Find the length
(d) What is the dimension
h(x) = 1 + x3 +x6
(a) Draw the linear
sequential circuit (LSC) that multiplies by the polynomial
g(x) = 1 + x2 + x4 +
x6 + x7
(b) Draw the linear
sequential circuit (LSC) that divides by the polynomial
(c) Draw the linear
sequential circuit (LSC) that simultaneously multiplies by h(x)
and divides by g(x).
Draw an LSC which takes as inputs polynomials
then produces the output h(x)a(x) +
k(x)b(x), where h(x)
are the polynomials:
h(x) = 1 + x4 + x10
= x + x2 + x4 + x7 + x9
Last Modified: April 4, 1998