1. Given codewords are 1000111, 0101011, and 0011101
Consider first 3 bits x1,x2 and x3 as data bits and last 4 bits c1,c2,c3 and c4 as parity bits.
By analysing pattern used to create parity bits here are-
x1 |
x2 |
x3 |
c1=x2⊕x3 |
c2=x1⊕x3 |
c3=x1⊕x2 |
c4=x1⊕x2⊕x3 |
1 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
other 5 codewords will be
0000000
0110110
1011010
1101100
1110001
Mininum distance = 4