# Digital Communications Questions and Answers – Cyclic Codes and Linear Block Codes

This set of Digital Communications Multiple Choice Questions & Answers (MCQs) focuses on “Cyclic codes and linear block codes”.

1. The cyclic codes are designed using
a) Shift registers with feedback
b) Shift registers without feedback
c) Flipflops
d) None of the mentioned

Explanation: The cyclic codes are a subclass of linear codes. It is designed using feedback shift registers.

2. A cyclic code can be generated using
a) Generator polynomial
b) Generator matrix
c) Generator polynomial & matrix
d) None of the mentioned

Explanation: A cyclic code can be generated using generator polynomial and block codes can be generated using generator matrix.

3. The feedback shift register circuit is called as
a) Multiplying circuit
b) Dividing circuit
c) Feedback circuit
d) Shifting circuit

Explanation: The cyclic shift of a code-word polynomial and encoding involves division of one polynomial by another. Thus this feedback shift register is also called as dividing circuit.

4. In the dividing circuit, the parity polynomial is obtained by the
a) Quotient
b) Remainder
c) Dividend
d) Divisor

Explanation: The parity polynomial is the remainder after diving by the generator polynomial it is available in the register after n shifts through the n-k stage feedback registers.

5. The received code contains an error if the syndrome vector is
a) Zero
b) Non zero
c) Infinity
d) None of the mentioned

Explanation: If the syndrome is an all zero vector then the received code-word is a valid code. If the syndrome is a non zero vector then the received code has errors.
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6. Block codes are generated using
a) Generator polynomial
b) Generator matrix
c) Generator polynomial & matrix
d) None of the mentioned

Explanation: Block codes are generated using generator matrix and cyclic codes are generated using generator polynomial.

7. Extended go-lay code is formed by
a) Adding overall parity bit to perfect go-lay code
b) Ex-oaring overall parity bit with perfect go-lay code
c) Ex-oaring each bit of go-lay code
d) Dividing the overall parity bit with perfect go-lay code

Explanation: Extended go-lay code is formed by adding overall parity bit with the perfect bit known as the golay code.

8. Block length is the _____________ in the code word.
a) Number of elements
b) Distance between elements
c) Number of parity bits
d) None of the mentioned

Explanation: The block length n is the number of elements in the code word.

9. The rate of a block code is the ration of
a) Block length to message length
b) Message length to block length
c) Message weight to block length
d) None of the mentioned

Explanation: The rate of a block code is the ratio between its message length and the block length, R=k/n.

10. Linear codes are used for
a) Forward error correction
b) Backward error correction
c) Forward error detection
d) Backward error detection

Explanation: Linear codes are used in forward error correction. It allows for more efficient encoding and decoding procedures.

11. The k-bit message forms ____ distinct messages which is referred to as k-tuples.
a) 2k
b) K2
c) 2k
d) 21/k

Explanation: The k bit messages for 2k distinct message sequences which are referred to as k-tuples or sequence of k digits.

12. The sum of any two vectors in subset S is also in S. This is called as
b) Subset property
c) Closure property
d) Similarity property

Explanation: The closure property states that the sum of any two vectors in subset S is also in S.

13. To avoid corruption during transmission, the code-word should be
a) Near
b) Far apart
c) Far
d) None of the mentioned

Explanation: The code-words should be far apart from one and another as possible so even when the vectors experience some corruption they may still be correctly decoded.

14. In a standard matrix set code-word there are _______ cosset.
a) 2k
b) 2n+k
c) 2n-k
d) 2n

Explanation: Each n-tuple appears in only one location none are missing and none are replicated. There are 2n-k cosets.

15. Syndrome is calculated by
a) HT/r
b) rHT
c) rH
d) None of the mentioned

Explanation: The syndrome is calculated using S=rHT.

16. The _____ of the code-word is the number of non zero elements.
a) Size
b) Weight
c) Distance
d) Subspace

Explanation: The size of the code-word is the number of code words. The weight of the code word can be given as the number of non zero elements and the distance between two code words is the hamming distance between them.

17. Some examples of linear codes
a) Hamming code
b) Reed-Solomon code
c) Parity code
d) All of the mentioned

Explanation: Some examples of linear codes are block codes, parity codes, reed-Solomon codes, hamming code, cyclic codes, polynomial codes, go-lay codes etc.

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