(a) Using the correspondence 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Chapter 8, Problem 12

(choose chapter or problem)

(a) Using the correspondence

\(\begin{array}{ccccccccccccccccccccccccccccccccccccccccccccc} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 & 21 & 22 & 23 & 24 & 25 & 26 & 27 \\ \mathrm{j} & \mathrm{k} & \mathrm{l} & \mathrm{n} & \mathrm{m} & \mathrm{s} & \mathrm{t} & \mathrm{u} & \mathrm{w} & \mathrm{x} & \mathrm{g} & \mathrm{h} & \mathrm{i} & \mathrm{o} & \mathrm{p} & \mathrm{q} & \mathrm{r} & \mathrm{v} & \mathrm{y} & \mathrm{z} & \mathrm{a} & \mathrm{b} & \mathrm{c} & \mathrm{d} & \mathrm{e} & \mathrm{f} & \text { space } \end{array} \)

find the numerical equivalent of the message

BUY ALL AVAILABLE STOCK AT MARKET.

(b) Encode the message by postmultiplying the message matrix M by

\(\mathbf{A}=\left(\begin{array}{rrr}1 & 1 & 0 \\1 & 0 & 1 \\1 & 1 & -1\end{array}\right)\).

(c) Verify your work by decoding the encoded message in part (b).