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University of California San Diego
ECE 259A:
Problem Set #1
0
. Send an email to
avardy@ucsd.edu
, stating your name, your general research interests, your
research advisor (if you have one), and what brings you to the course on algebraic coding theory.
1
. An
erasure
is an error whose location is known. Prove that a code
over
q
with minimum dis
tance
d
can correct
τ
errors and
σ
erasures, provided
d
2
1
.
2
. Find all the binary linear MDS codes. Prove your answer.
3
. Consider the binary linear code de±ned by the generator matrix
G
1 0 1 1 1 0 0
1 1 1 1 1 0 1
0 1 1 0 1 1 1
(a) Find a generator matrix for this code in systematic form.
(b) Find a parity check matrix for this code.
(c) What is the minimum distance of this code?
4
. Let
be an
n
,
k
, 2
t
1
binary linear code with parity check matrix
H
. Let
be a code of
length
n
1
obtained by appending to all the codewords
x
x
1
,
x
2
, . . .
x
n
an overall par
itycheck bit equal to
x
1
x
2
x
n
.
(a) Find the parameters of
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 Fall '08
 Prof.AlexanderVardy

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