Figure 1.12 shows the performance of repetition codes and the Hamming code. It also shows the performance of a family of linear block codes that are generalizations of Hamming codes, `BCH' codes.
Figure: Error probability 
versus rate for repetition codes,
the (7,4) Hamming code and BCH codes with block lengths up to 1023
over a binary symmetric channel with f=0.1.
The right hand figure shows on a logarithmic scale.
This figure shows that we can, using linear block codes, achieve better
performance than repetition codes; but the asymptotic situation still
looks rather grim.
Design an error correcting code and a decoding algorithm for it,
compute its probability of error,
and add it to figure 1.12.