Please assist in completing the enclosed assignment.  Thanks in advanced.

 

 

Student: Benny Jones Date: 7/19/16 Instructor: Thara Lowndes Course: Math 101 ­Summer 2016­Sec.
953 (Choden) 1. Suppose that the generator matrix for a (4,8)­code is:
1 0 0 0 1 0 1 0
0 1 0 0 0 1 0 1
0 0 1 0 0 1 1 0
0 0 0 1 1 0 0 1
The codeword corresponding to 1010 is . 2. Suppose that the generator matrix for a (4,8)­code is:
1 0 0 0 1 0 1 0
0 1 0 0 0 1 0 1
0 0 1 0 0 1 1 0
0 0 0 1 1 0 0 1
The codeword corresponding to 1101 is . 3. Determine all the codewords for the code having the generator matrix:
1 0 1 0 1
0 1 1 1 0
List all possible codewords, separated by commas: . 4. Determine all the check matrix associated with the generator matrix:
1 0 1 1 0
0 1 0 0 1
Using the table, correctly fill in the check matrix values: Assignment: HW 15­Matrix Codes (7.3 &
7.4) 5. Determine the check matrix associated with the generator matrix:
1 0 0 1 1 0
0 1 0 0 0 0
0 0 1 1 0 1
Using the table, correctly fill in the check matrix values. 6. The given codeword was received after being decoded using the generator matrix and transmitted. 1 0 0 1 0 1 0
0 1 0 0 1 1 0
0 0 1 1 1 0 1
Determine the syndrome of the word 1001110 , and decode if it is a codeword or if it differs from a codeword in a single digit. The syndrome is . If a codeword, enter the codeword. If not a codeword enter 0. 7. The given codeword was received after a message was encoded using the generator matrix 1 0 0 1 0 1 0
0 1 0 0 1 1 0
0 0 1 1 1 0 1
and then transmitted. Determine the syndrome of the received word 1110100 , and decode it if it is a codeword or if it differs from a codeword in a single digit.
The syndrome is The original message was . (if the word cannot be decoded, enter 'unknown'). 8. Determine the syndrome of each word using the check matrix:
1 0 0 1
0 1 1 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
Decode 110011 and give the syndrome and codeword.
The syndrome is and the message is (if not a codeword enter 0). 9. Determine the syndrome of each word using the check matrix:
1 0 0 1
0 1 1 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
Decode 011111 and give the syndrome and codeword.
The syndrome is and the message is (if not a codeword enter 0).

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