This question is about the Hadamard code corresponding to the 16 × 16 Hadamard matrix created by Sylvester's Construction. Create a 5-digit number by writing the last five digits of your enrolment number. So for example, with enrolment number 000123456 I would create 23456. Now create a 5-bit message by converting each of these digits to the equivalent (mod 2), so even numbers are written as 0 and odd numbers as 1- here I would write 01010. If your message contains 1 or fewer 1s, make both the first and last bit into 1, so that you have a 5-bit message containing at least two 1s. (a) Write down the Hadamard matrix and say how the 32 codewords are obtained from it.
This question is about the Hadamard code corresponding to the 16 × 16 Hadamard matrix created by Sylvester's Construction. Create a 5-digit number by writing the last five digits of your enrolment number. So for example, with enrolment number 000123456 I would create 23456. Now create a 5-bit message by converting each of these digits to the equivalent (mod 2), so even numbers are written as 0 and odd numbers as 1- here I would write 01010. If your message contains 1 or fewer 1s, make both the first and last bit into 1, so that you have a 5-bit message containing at least two 1s. (a) Write down the Hadamard matrix and say how the 32 codewords are obtained from it.
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
my enrolment number
Which is 001055536

Transcribed Image Text:3.
This question is about the Hadamard code corresponding to the 16 x 16 Hadamard
matrix created by Sylvester's Construction.
Create a 5-digit number by writing the last five digits of your enrolment number. So
for example, with enrolment number 000123456 I would create 23456. Now create a
5-bit message by converting each of these digits to the equivalent (mod 2), so even
numbers are written as 0 and odd numbers as 1- here I would write 01010. If your
message contains 1 or fewer 1s, make both the first and last bit into 1, so that you
have a 5-bit message containing at least two 1s.
(a)
Write down the Hadamard matrix and say how the 32 codewords are
obtained from it.
(b)
Write out the generating matrix and the decoding matrix for this code.
(c)
Carry out the matrix operations to encode your 5-bit message and to decode
the resulting codeword.
(d)
What is the distance of this code? What is its rate? How many errors can it
correct?
(e)
Give an example of a word which differs from your encoded message in as
many places as possible while still being nearer to your encoded message
than to any other codeword.
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 3 steps with 1 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