Chapter 8.5, Problem 49E

(a)

To determine

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

Answer to Problem 49E

Uncoded matrices for the given massage are,

  $\left[12114\right],\left[4914\right],\left[7019\right],\left[2133\right],\left[51919\right],\left[62112\right]$

Explanation of Solution

Given information:

Given massage

LANDING SUCESSFUL

Given matrix

  $A=\left[\begin{array}{ccc}1& 2& 2\\ 3& 7& 9\\ -1& -4& -7\end{array}\right]$

Calculation:

We have to first the $1\times 3$ encoding matrix.

We split the massage into groups two:

“L A N” “D I N” “G _ S” “U C C” “E S S” “F U L”

12 1 14 4 9 14 7 0 19 21 3 3 5 19 19 6 21 12

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

  $\left[12114\right],\left[4914\right],\left[7019\right],\left[2133\right],\left[51919\right],\left[62112\right]$

(b)

To determine

To encode: the massage using the encoding matrix.

Answer to Problem 49E

The following cryptogram,

1 -25 65 17 15 -9 -12 -61 -119 27 51 48 43 67 48 57 111 117.

Explanation of Solution

Calculation:

Now to get the coded row matrices,

Uncoded matrix Encoding matrix coded matrix

  $\begin{array}{c}\left[12114\right]\left[\begin{array}{ccc}1& 2& 2\\ 3& 7& 9\\ -1& -4& -7\end{array}\right]\left[1-2565\right]\\ \left[4914\right]\left[\begin{array}{ccc}1& 2& 2\\ 3& 7& 9\\ -1& -4& -7\end{array}\right]\left[17156-9\right]\\ \left[7019\right]\left[\begin{array}{ccc}1& 2& 2\\ 3& 7& 9\\ -1& -4& -7\end{array}\right]\left[-12-61-119\right]\\ \left[2133\right]\left[\begin{array}{ccc}1& 2& 2\\ 3& 7& 9\\ -1& -4& -7\end{array}\right]\left[275148\right]\\ \left[51919\right]\left[\begin{array}{ccc}1& 2& 2\\ 3& 7& 9\\ -1& -4& -7\end{array}\right]\left[436748\right]\\ \left[62112\right]\left[\begin{array}{ccc}1& 2& 2\\ 3& 7& 9\\ -1& -4& -7\end{array}\right]\left[57111117\right]\end{array}$

So the sequence of coded row matrices

  $\left[1-2565\right],\left[1715-9\right],\left[-12-61-119\right],\left[275148\right],\left[436748\right],\left[57111117\right]$

Finally removing the matrix notation produces the following cryptogram,

1 -25 65 17 15 -9 -12 -61 -119 27 51 48 43 67 48 57 111 117.