Consider the (6,3) binary linear block code defined by the following generator matrix: 1 1 1 G = 1 1 1 1 1 1. Eind the narity-check matrix H.
Consider the (6,3) binary linear block code defined by the following generator matrix: 1 1 1 G = 1 1 1 1 1 1. Eind the narity-check matrix H.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
![**Problem 8: Binary Linear Block Code**
Consider the (6,3) binary linear block code defined by the following generator matrix:
\[
G = \begin{bmatrix}
0 & 1 & 1 & 1 & 0 & 0 \\
1 & 0 & 1 & 0 & 1 & 0 \\
1 & 1 & 0 & 0 & 0 & 1
\end{bmatrix}
\]
**Tasks:**
(a) Find the parity-check matrix \( H \).
(b) Assume that the correctible error patterns are all 1-bit error patterns and a 2-bit error pattern \( 010001 \). Decode the received vector \( \mathbf{r} = (111101) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbffa73e6-1761-4c9e-97cb-0c164f013989%2F7fdd9fb3-7fe7-49d1-9c79-bded010e30bb%2Fj6xaf_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 8: Binary Linear Block Code**
Consider the (6,3) binary linear block code defined by the following generator matrix:
\[
G = \begin{bmatrix}
0 & 1 & 1 & 1 & 0 & 0 \\
1 & 0 & 1 & 0 & 1 & 0 \\
1 & 1 & 0 & 0 & 0 & 1
\end{bmatrix}
\]
**Tasks:**
(a) Find the parity-check matrix \( H \).
(b) Assume that the correctible error patterns are all 1-bit error patterns and a 2-bit error pattern \( 010001 \). Decode the received vector \( \mathbf{r} = (111101) \).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Recommended textbooks for you
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education