The number of code word possible using the generator \(G = \begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \end{bmatrix}\) is :
4
A generator matrix with k linearly independent rows produces a linear code whose code words are all GF(2) combinations of those rows, giving \(2^{k}\) code words.
Here G has 2 rows, 110 and 011, which are linearly independent (neither is the zero word and they differ), so k = 2.
The code words are 000, 110, 011 and 110 ⊕ 011 = 101, i.e. \(2^{2} = 4\) words.
The value 8 would be the count of all 3-bit words \(2^{3}\), while 1 and 2 ignore the combinations of the rows.
Check: listing messages 00, 01, 10, 11 and multiplying by G gives 000, 011, 110, 101, four distinct code words.
Hence, 4.
Similar Questions
Let \(\varphi, \psi\) be the formula, \(\varphi \models \Psi\), if and only if \(\varphi \models \Psi\) is a :
Which of the following relations defined on X = {1, 2, 3} is an equivalent relation ?
A rod is divided into six segment is to be colored with one or more of 4 different colors. In how many ways can this be done ?
Consider the following linear programming problem : Maximize \(z = 5x_{1} + 2x_{2} + 3x_{3} - x_{4} + x_{5}\) Subject to : \(x_{1} + 2x_{2} + 2x_{3} + x_{4} = 8\), \(3x_{1} + 4x_{2} + x_{3} + x_{5} = 7\), \(x_{1}, x_{2}, x_{3}, x_{4}, x_{5} \geq 0\) What will be the basic feasible solution after iteration 1 ?
The thickness of a graph G is defined as minimum number of (edge-disjoint) planar subgraphs into which G can be decomposed. The thickness of G is defined as \(\theta(G)\). What is the thickness of planar graph ?
A committee is to be selected from 5 candidates a, b, c, d and e. The selection must satisfy all the following conditions :
• Either a or b must be included, but not both
• Either c or e or both must be included
• If d is included then b must be included
• Either a or c are included or neither is included.
• If e is included, then c and d must be included. How should selection be made ?
Let us consider the letters from a through h, and all 5 letters are made using these letters. (words are just strings of letters). How many of these words contain no repeated letters ?
Let us consider the following primal problem : Maximize \(z = 2x_{1} + x_{2}\) Subject to \(x_{1} - x_{2} \leq 4\), \(x_{1} - x_{2} \leq 2\), \(x_{1}, x_{2} \geq 0\) What will be its dual problem ?
Identify an appropriate operation sequence with respect to execution of a machine level language instruction.
The “instruction decode” phase in CPU’s instruction cycle is responsible to _____ .
Important Questions from Mixed Topic (MH-SET)
.................... is a client server application that identifies each host on the internet with a unique user-friendly name.
Every OS has a ................ or .......... which primarily resides in the main memory of the computer to perform some of the basic functions of the OS.
(i) Kernel
(ii) Interface
(iii) Nucleus
(iv) Compiler
Codes:
Which of the following are referred to as low level language?
(i) Machine language
(ii) Assembly language
(iii) High level language
(iv) Natural language
Codes:
Match the following:
List I List II (a) New York Public Library (i) Shelv AR (b) Miami University Augmented Research Group (ii) Smart library (c) Oula University Library (iii) Wolf Walk (d) North Carolina State University (iv) Find the future Codes:
Which part of the QR code represents the encoded data?
