Please do all of #5 step by step on notebook paper. Thank you.

Thamas - x C Chegg Study Guided Sex C O Secure Main MCS 425 Codes written-1(1).png (1638 https://uic.blackboard.com/bbcswebdav/pid-5876915-dt-content-rid-61006944_2/courses/2018.spring.mcs.425,36866/written-1%281%29.png 8 3. The following is a parity check matrix for a binary [n, le code C: ( 1 1 1 0 0 | 10 O 10. 0 1 0 0 1 ) (a) Find n and k. (b) Find the generator matrix for C. (c) List the codesords in C. (d) What is the code rate for C? 4. Let C = {(0,0,0), (1, 1, 1)} be a binary repetition code. (a) Find a parity check matrix for C. (b) List the cosets and coset leaders for C. (c) Find the syndrome for each coset. (d) Suppose you receive the message (1, 1, 0). Use the syndrome de- coding method to decode it. 6. Lct C be the binary code {(0,0,1), (1, 1, 1), (1,0,0), (0, 1,0)}. (a) Show that C is not linear. (b) What is d(C)? (Since C is not linear, this cannot be found by calculating the minimum weight.) (c) Show that C satisfies the Singleton bound with equality. LO e 9 H G Me P O 10:31 AM Type here to search 1/22/2018 Thamas - x C Chegg Study Guided Sex C O Secure Main MCS 425 Codes written-1(1).png (1638 https://uic.blackboard.com/bbcswebdav/pid-5876915-dt-content-rid-61006944_2/courses/2018.spring.mcs.425,36866/written-1%281%29.png 8 3. The following is a parity check matrix for a binary [n, le code C: ( 1 1 1 0 0 | 10 O 10. 0 1 0 0 1 ) (a) Find n and k. (b) Find the generator matrix for C. (c) List the codesords in C. (d) What is the code rate for C? 4. Let C = {(0,0,0), (1, 1, 1)} be a binary repetition code. (a) Find a parity check matrix for C. (b) List the cosets and coset leaders for C. (c) Find the syndrome for each coset. (d) Suppose you receive the message (1, 1, 0). Use the syndrome de- coding method to decode it. 6. Lct C be the binary code {(0,0,1), (1, 1, 1), (1,0,0), (0, 1,0)}. (a) Show that C is not linear. (b) What is d(C)? (Since C is not linear, this cannot be found by calculating the minimum weight.) (c) Show that C satisfies the Singleton bound with equality. LO e 9 H G Me P O 10:31 AM Type here to search 1/22/2018