(a) (i) Write down a parity-check matrix for the code Ham(2, 7). (ii) Using your parity-check matrix, explain why the minimum distance of Ham(2, 7) is exactly 3. (b) Consider the linear code C over F, with the following parity-check matrix: (3 1 1 0 2 30 1 (i) Decide whether or not C is an MDS code. Justify your answer. (ii) Suppose that the above matrix is instead taken to be the generator matrix of a linear code D over F7. Is D an MDS code? Justify your answer.
(a) (i) Write down a parity-check matrix for the code Ham(2, 7). (ii) Using your parity-check matrix, explain why the minimum distance of Ham(2, 7) is exactly 3. (b) Consider the linear code C over F, with the following parity-check matrix: (3 1 1 0 2 30 1 (i) Decide whether or not C is an MDS code. Justify your answer. (ii) Suppose that the above matrix is instead taken to be the generator matrix of a linear code D over F7. Is D an MDS code? Justify your answer.
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Question
![(a) (i) Write down a parity-check matrix for the code Ham(2, 7).
(ii) Using your parity-check matrix, explain why the minimum distance of
Ham(2, 7) is exactly 3.
(b) Consider the linear code C over F, with the following parity-check matrix:
(3 1 1 0
2 30 1
(i) Decide whether or not C is an MDS code. Justify your answer.
(ii) Suppose that the above matrix is instead taken to be the generator matrix of
a linear code D over F7. Is D an MDS code? Justify your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8f66d409-6ee9-4af3-88e7-6dbb4539d98a%2F6e767786-50d0-465e-85db-d71df13fde80%2Fbqy4p4m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) (i) Write down a parity-check matrix for the code Ham(2, 7).
(ii) Using your parity-check matrix, explain why the minimum distance of
Ham(2, 7) is exactly 3.
(b) Consider the linear code C over F, with the following parity-check matrix:
(3 1 1 0
2 30 1
(i) Decide whether or not C is an MDS code. Justify your answer.
(ii) Suppose that the above matrix is instead taken to be the generator matrix of
a linear code D over F7. Is D an MDS code? Justify your answer.
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