Chapter 8.5, Problem 51E

(a)

To determine

To write: the uncoded $1\times 3$ row matrices for the massage.

Answer to Problem 51E

Uncoded matrices for the given massage are,

  $\left[3112\right],\left[12013\right],\left[5020\right],\left[151315\right],\left[181815\right],\left[2300\right]$

Explanation of Solution

Given information:

Given massage

CALL ME TOMORROW

Given matrix

  $\left[\begin{array}{ccc}1& -1& 0\\ 1& 0& -1\\ -6& 2& 3\end{array}\right]$

Calculation:

First create the $1\times 3$ encoding matrix.

We split the massage into groups two:

“CAL” “L_M” “E_T: “O M O” “R R O” “W__”

3 1 12 12 0 13 5 0 20 15 13 15 18 18 15 23 0 0

Thus the set of uncoded matrices for the given massage are,

  $\left[3112\right],\left[12013\right],\left[5020\right],\left[151315\right],\left[181815\right],\left[2300\right]$

(b)

To determine

To encode: the massage using the encoding matrix.

Answer to Problem 51E

The following cryptogram,

-68 21 -35 -66 14 39 -115 35 60 -62 15 32 -54 12 27 23 -23 0.

Explanation of Solution

Calculation:

Now to get the coded row matrices,

Uncoded matrix Encoding matrix coded matrix

  $\begin{array}{c}\left[3112\right]\left[\begin{array}{ccc}1& -1& 0\\ 1& 0& -1\\ -6& 2& 3\end{array}\right]\left[-682135\right]\\ \left[12013\right]\left[\begin{array}{ccc}1& -1& 0\\ 1& 0& -1\\ -6& 2& 3\end{array}\right]\left[-661439\right]\\ \left[5020\right]\left[\begin{array}{ccc}1& -1& 0\\ 1& 0& -1\\ -6& 2& 3\end{array}\right]\left[-1153560\right]\\ \left[151315\right]\left[\begin{array}{ccc}1& -1& 0\\ 1& 0& -1\\ -6& 2& 3\end{array}\right]\left[-621532\right]\\ \left[181815\right]\left[\begin{array}{ccc}1& -1& 0\\ 1& 0& -1\\ -6& 2& 3\end{array}\right]\left[-541227\right]\\ \left[2300\right]\left[\begin{array}{ccc}1& -1& 0\\ 1& 0& -1\\ -6& 2& 3\end{array}\right]\left[23-230\right]\end{array}$

So the sequence of coded row matrices

  $\left[-682135\right],\left[-661439\right],\left[-1153560\right],\left[-621532\right],\left[-541227\right],\left[23-230\right]$

Finally removing the matrix notation produces the following cryptogram,

-68 21 -35 -66 14 39 -115 35 60 -62 15 32 -54 12 27 23 -23 0