Linear Block Codes
Linear block codes are a type of error detection and correction codes used in communication systems. They are characterized by their ability to detect and correct errors in the received data.

Error Detection and Correction
Error detection refers to the ability of a code to detect the presence of errors in the received data. Error correction, on the other hand, refers to the ability of a code to not only detect errors but also correct them.

Minimum Hamming Distance
The minimum Hamming distance of a code is defined as the minimum number of bit positions in which any two valid code words differ. In other words, it is the minimum number of errors that need to occur in a code word for it to be mistaken for another valid code word.

Given Information
In the given question, it is known that the linear block code can detect 2 errors and can correct only 1 error. We need to determine the minimum Hamming distance for this code.

Explanation
To understand why the correct answer is option 'A' (4), let's consider the following scenarios:

1. If the minimum Hamming distance is 1, it means that two valid code words can differ in only one bit position. In this case, if an error occurs in one bit position, the received code word can be mistaken for another valid code word. However, the code is only capable of correcting 1 error, so it would fail to correct this situation. Therefore, the minimum Hamming distance cannot be 1.

2. If the minimum Hamming distance is 2, it means that two valid code words can differ in two bit positions. In this case, if two errors occur in different bit positions, the received code word can be mistaken for another valid code word. The code is capable of detecting 2 errors, so it would be able to detect this situation. However, it can only correct 1 error, so it would fail to correct this situation. Therefore, the minimum Hamming distance cannot be 2.

3. If the minimum Hamming distance is 3, it means that two valid code words can differ in three bit positions. In this case, even if three errors occur in different bit positions, the received code word can still be uniquely identified as the correct code word. The code is capable of detecting 2 errors, so it would be able to detect this situation. However, it can only correct 1 error, so it would fail to correct this situation. Therefore, the minimum Hamming distance cannot be 3.

4. If the minimum Hamming distance is 4, it means that two valid code words can differ in four bit positions. In this case, if four errors occur in different bit positions, the received code word can still be uniquely identified as the correct code word. The code is capable of detecting 2 errors, so it would be able to detect this situation. It can also correct 1 error, so it would be able to correct any single error. Therefore, the minimum Hamming distance must be 4.

Hence, the correct answer is option 'A' (4).