The minimum distance required for a linear block code to achieve a guaranteed correction of up to 5 errors is

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  1. 6
  2. 5
  3. 11
  4. 10

Answer (Detailed Solution Below)

Option 3 : 11
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Concept:

Hamming distance between two words of the same size is the number of differences between the corresponding bits. It can be calculated by applying the XOR operation.

Formula:

To guarantee the correction of up to s errors in all cases, the hamming distance in a block code must be d ≥ 2s + 1

Let hamming distance be minimum

∴ dmin = 2s + 1

Calculation

number of errors = s = 5.

∴ dmin = 2(5) + 1 = 11

Important Point:

Minimum Hamming distance is the smallest hamming distance between all possible pairs in a set of words. There are three parameters in this: codeword size, data word size, and minimum Hamming distance. When a codeword is corrupted during transmission, the hamming distance between sent and the received codeword is the number of bits affected by the error.

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