Play with code-1

1

100

If a C is a valid Code vector, and H is Parity check matrix, then C. H^T= 0.  Agree/ Disagree.

Agree

200

The set G is closed under the binary operation . , which is referred to as modulo-p multiplication. The p should be .... number

prime

300

i. Every element in G appears in one and only one coset of H

ii. All the distinct cosets of H are disjoint; and 

iii. The union of all the distinct cosets of H forms the group G. 

What they refer to ?

Properties of Cosets

400

Finite fields are also called Galois fields, in honour of their discoverer. Who is the Discoverer?

Évariste Galois

500

1 = -1? In which arithmetic

Modulo-2

2

100

d_min-1

Error detecting capability of Block code

200

Number of elements in the field is the ……… of the field.

Order

300

Any irreducible polynomial over GF(2) of degree m divides

[X^((2^m)-1)] +1

400

The number of vectors in a basis of a vector space is called the ..... of the vector space. 

dimension

500

In dividing circuit of cyclic codes, the parity polynomial is obtained by the _____Polynomial

Reminder

3

100

k x (n-k) in Linear Block code (n ,k)

Size of parity matrix

200

The following parameter refers to

Code length: n = 2^m -L -1 

Number of information symbols: k = 2^m - m -L-1 

Number of parity-check symbols: n — k = m 

Error-correcting capability: dmjn >= 3. 

Shortened Hamming Codes

300

Considering GF (7), Subtraction (4-5) is

6

400

Considering the property of polynomials over GF(2)  [f(X)]^(2^l)=f(X^2ⁱ) , 

f(x)= X^16+X^12+1, Then what is the value of n in the expression

f(x))=(X⁴ + X³ + l)ⁿ 

 

4

f(x))=(X4 + X3 + l)⁴

500

X³ + X + 1 divides..... polynomial

X⁷ +1

4

100

A zero syndrome represents

No Error

200

The characteristic Lamda of a finite field is prime.True/False

True

300

n = 32, k(2, 5) = 16, d_min of RM code

d_min = 2^m-r = 8

400

The Generator matrix of (24,12) Golay code is....

G=[ P I₁₂ ]

500

The minimal polynomial of an element Beta in GF(2^m) devides

X^{2^m} + X

5

100

A primitive polynomial must be an irreducible polynomial. Agree or Disagree.

Agree

200

An (n, k) linear code C is called a cyclic code if every ...... of a codeword in C is also a codeword in C. 

cyclic shift

300

The code polynomial of  code word is (1001011).... 

1 + X³ + X⁵ + X⁶ 

400

The syndrome 

so = r0 ₊ r3 + r5 + r6 

s1 = r1 + r3 + r4 + r5 

s2 = r2 + r4 + r5 + r6

Then the  parity matrix is ..

[1 1 0  

 0 1 1

 1 1 1

 1 0 1]

500

The elements of V are called vectors, and the elements of the field F are called .... The addition on V is called a .....  addition, and the multiplication that combines a scalar in F and a vector in V into a vector in V is referred to as .... (or product). 

scalars, vector, scalar multiplication