Linear Code and Code Words
Linear code is a type of error-correcting code that can be represented as a linear combination of its code words. It is used to detect and correct errors that may occur during data transmission. A code word is a sequence of bits that represents a message that has been encoded with a particular code.

Given code words are (0011, 0101, 1010) in a linear code, and we need to identify which of the given options is not a code word of the linear code.

Explanation
To check if a sequence of bits is a code word of a linear code, we can use the following steps:

Step 1: Create a generator matrix for the linear code.
A generator matrix is a matrix that contains all the code words of a linear code. In this case, the generator matrix would be:

G = | 0 0 1 1 |
| 0 1 0 1 |
| 1 0 1 0 |

Step 2: Multiply the sequence of bits by the generator matrix.
To do this, we need to represent the sequence of bits as a row vector, and then multiply it by the generator matrix. If the result is a multiple of the code word, then the sequence of bits is a code word of the linear code.

For example, let's check if 0110 is a code word of the linear code:

0110 * G = | 0 1 1 1 |

This is not a multiple of any of the code words in the generator matrix, so 0110 is not a code word of the linear code.

Similarly, we can check the other options:

1001 * G = | 1 1 1 0 | (not a multiple of any code word)
1111 * G = | 0 0 0 0 | (a multiple of 0000, which is a code word)
0001 * G = | 1 0 0 1 | (not a multiple of any code word)

Thus, option D (0001) is not a code word of the linear code.

Conclusion
Linear codes are a type of error-correcting codes that can detect and correct errors that may occur during data transmission. To check if a sequence of bits is a code word of a linear code, we can use a generator matrix and multiply the sequence of bits by it. If the result is a multiple of any of the code words in the generator matrix, then the sequence of bits is a code word of the linear code.