5. Linear codes The code words U1 001010, u2111101, 43 001001, u4 = 101111. form a basis for a (6,4) linear binary code. i. Write down a generator matrix for this code. ii. Construct code words for the messages 1110, 1001 and 0110. iii. Write down the parity check matrix for this code. iv. Find syndromes for the received words 101010, 100101 and 001110.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
icon
Related questions
Question

Q 8 

5. Linear codes
The code words
U₁ =
001010, u₂ = 111101, u3 = 001001, u4101111.
form a basis for a (6,4) linear binary code.
i. Write down a generator matrix for this code.
ii. Construct code words for the messages 1110, 1001 and 0110.
iii. Write down the parity check matrix for this code.
iv. Find syndromes for the received words 101010, 100101 and 001110.
Transcribed Image Text:5. Linear codes The code words U₁ = 001010, u₂ = 111101, u3 = 001001, u4101111. form a basis for a (6,4) linear binary code. i. Write down a generator matrix for this code. ii. Construct code words for the messages 1110, 1001 and 0110. iii. Write down the parity check matrix for this code. iv. Find syndromes for the received words 101010, 100101 and 001110.
Expert Solution
steps

Step by step

Solved in 2 steps with 6 images

Blurred answer
Similar questions
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education