- Reading Assignment
- MacWilliams & Sloane, Chap. 4
- Peterson & Weldon, Chap. 6
-
Problem 1.
The polynomial
p(x) = x6 + x5 + 1
is primitive (hence, irreducible) over
GF(2)
. Use
p(x)
to constructa log/antilog table for
GF(26)
.
-
Problem 2.
The polynomial
p(x) = x2 + x + 2
is primitive (hence, irreducible) over
GF(3)
. Use
p(x)
to constructa log/antilog table for
GF(32)
.
-
Problem 3.
Let
R
be a commutative ring with non-zero elements
a
and
b
such that
ab = 0
Prove that
R
is not a field.
-
Problem 4.
A degree 4 irreducible polynomial
p(x)
in Peterson's Table of Irreducible Polynomials over
DEGREE 4 ... 3 37D ...
- What is p(x)?
p(x)= ...
- Since p(x) is irreducible and
of degree 4, it follows that
GF(24) = GF(2)[x] mod p(x)
List all the elements of GF(24)
in the above representation, i.e., in terms of
ksi = x mod p(x).
- Let ksi = x mod p(x).
Why is { ksik} not a
complete list of all the non-zero elements of
GF(24)?