University of Illinois
Fall 2005
ECE 556:
Second MidSemester Exam
Thursday November 17, 2005, 8:30 a.m. – 9:50 a.m.
This is a opentext openhandwrittennotes examination. No
printed materials
other than the
textbook and Problem Sets and Solutions distributed in class are permitted. Calculators, laptop
computers, PDAs, iPods, cellphones, email pagers, etc. are neither needed nor permitted.
This Examination contains three problems
1
. Let
m
denote an even integer,
α
a primitive element of GF(2
m
), and
β
=
α
1+2
m/
2
.
(
a
) Show that
β
is a primitive element of the
subﬁeld
GF(2
m/
2
).
(
b
) What is the BCH bound on the minimum distance of the lowrate binary cyclic code
of length 2
m

1 whose
paritycheck
polynomial
h
(
x
) is
M
α
(
x
)
M
β
(
x
)? Here, as usual,
M
α
(
x
) and
M
β
(
x
) are the minimal polynomials of
α
and
β
over GF(2).
2
. Let
α
denote a primitive element of GF(2
5
) with minimal polynomial
x
5
+
x
2
+1, and consider
a 5errorcorrecting
binary
BCH code of length 31. Suppose that the syndrome polynomial
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 02/08/2012 for the course ECE 556 taught by Professor Milenkovic,o during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Milenkovic,O

Click to edit the document details