This preview shows page 1. Sign up to view the full content.
Math 810, Spring 2011 – HW 3
Due Wednesday, 2 March 2011
1. (
a
) Give a syndrome table (syndrome dictionary) for the [9
,
5] binary linear
code
E
with the following check matrix:
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
.
(
b
) Use your table to decode the received word:
(0
,
1
,
0
,
1
,
1
,
0
,
0
,
0
,
0)
.
(
c
) Use your table to decode the received word:
(1
,
1
,
1
,
0
,
1
,
1
,
0
,
1
,
0)
.
2. Let
H
be a check matrix for the binary linear code
C
. Assume that the
columns of
H
This is the end of the preview. Sign up
to
access the rest of the document.
Unformatted text preview: are nonzero and distinct. Additionally assume that each column of H contains an odd number of 1’s. Prove that d min ( C ) ≥ 4. 3. Let D be a linear ternary code (that is, a linear code over F 3 ). Prove that either all of the codewords begin with 0 or exactly 1 / 3 of the codewords begin with 0....
View
Full
Document
This note was uploaded on 06/13/2011 for the course CRYPTO 101 taught by Professor Na during the Spring '11 term at Harding.
 Spring '11
 NA

Click to edit the document details