# Decoding used in Algorithms

Using a transposition matrix of size 4 by 6 (4 columns, 6 rows) and key ‘time’ decode the following message:

RLAPET HWBUIE EIERSS TELSRT

I am just looking for either a starting point or a step by step guide through the question please.

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As it stands this question is rather light on context to expect a good answer. If you have the definitions then it should just be a case of working through them. If you don't, go back to the person who set the question and complain. – Peter Taylor Feb 25 '13 at 18:25

## 1 Answer

You’re told that the key is time. This means that the message was written by rows into an array with four columns; since there are $24$ letters, this took six rows. The key time was written at the top of the array, so that the t was above the first column, the i above the second column, and so on. Finally, the letters were read out one column at a time, taking the columns in alphabetical order of the letters in the keyword. Thus, the fourth column, under the e of time, was read out first, and the first column, under the t, was read out last.

If the message had been This is my note, the initial setup would have looked like this:

time
----
THIS
ISMY
NOTE


The letters of time in alphabetical order are eimt, so I now read off columns $4$, $2$, $3$, and $1$ in that order to produce SYE HSO IMT TIN.

To decipher the given message, reverse the procedure. RLAPET is the first column read out, so it must be the e (fourth) column of the original array:

time
----
R
L
A
P
E
T


HWBUIE was the second column read out, so it must be the i (second) column of the original array:

time
----
H R
W L
B A
U P
I E
E T


Continuing in this fashion, we reconstruct the entire initial array:

time
----
THER
EWIL
LBEA
SURP
RISE
TEST


The original message was filled in by rows, so it must have been THEREWILLBEASURPRISETEST, and you’ll have no trouble supplying the correct word divisions.

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