Lecture
Build a set of code words .
If a generating matrix is specified, then the entire set of code words can be obtained by all possible linear combinations of rows of the matrix. For G 1, we construct all code words:
V 1 | V 1 ΘV 2 | V 1 ΘV 2 ΘV 3 |
V 2 | V 1 ΘV 3 | V 1 ΘV 2 ΘV 4 |
V 3 | V 1 ΘV 4 | V 2 ΘV 3 ΘV 4 |
V 4 | V 2 ΘV 3 | V 1 ΘV 3 ΘV 4 |
V 2 ΘV 4 | V 1 ΘV 2 ΘV 3 ΘV 4 | |
V 3 ΘV 4 | ||
1000110 | 1100011 | 1110000 |
0100101 | 1010101 | 1101100 |
0010011 | 1001001 | 0111001 |
0001111 | 0110110 | 1011010 |
0101010 | 1111111 | |
0011100 |
and 0000000.
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Information and Coding Theory
Terms: Information and Coding Theory