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23:  We need a dataword of at least 11 bits. Find the values of k and n in the Hamming
code C(n, k) with dmin :3.

 

Soln: We need to find k = 2m −1 − m ≥ 11. We use trial and error to find the right
answer:
a. Let m = 1 k = 2m −1 − m = 21 −1 − 1 = 0 (not acceptable)
b. Let m = 2 k = 2m −1 − m = 22 −1 − 2 = 1 (not acceptable)
c. Let m = 3 k = 2m −1 − m = 23 −1 − 3 = 4 (not acceptable)
d. Let m = 4 k = 2m −1 − m = 24 −1 − 4 = 11 (acceptable)
Comment: The code is C(15, 11) with dmin = 3.

How this n=15 came?? please explain
 

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