1. Compare the parity-check matrix of the (7,4) Hamming code considered in Example 1 with that of a (4,1) repetition code
2. Consider the (7,4) Hamming code of Example 1. The generator matrix G and the parity-check matrix H of the code are described in that example. Show that these two matrices satisfy the condition
EXAMPLE 1
Binary Sequence for Energy Calculations Consider the five-digit binary sequence 10010. This sequence is represented by two different waveforms, one based on the rectangular function rect(t), and the other based on the sinc function sinc(t).
Despite this difference, both waveforms are denoted by g(t), which implies they both have exactly the same total energy, to be demonstrated next.