Question

Using the encoding matrix `[(1,1),(0,1)]` encode and decode the messag I*LOVE*MUMBAI.

Answer 1

A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	*	Y	Z
1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	27	25	26

I	*	L	O	V	E	*	M	U	M	B	A	I	*
9	27	12	15	22	5	27	13	21	13	2	1	9	27

Encoding the message includes the following process.

`[(1,1),(0,1)][(9,12,22,27,12,2,9),(27,15,5,13,13,1,27)]`

`=[(9+27,12+15,22+5,27+13,12+13,2+1,9+27),(27,15,5,13,13,1,27)]`

`=[(36,27,27,40,25,3,36),(27,15,5,13,13,1,27)]`

Hence the encoded message we get as,

36, 27, 27, 15, 27, 5, 40, 13, 25, 13, 3, 1, 36, 27.

Now the process of decoding is as follows.

Inverse of `[(1,1),(0,1)]` is `[(1,-1),(0,1)]`

`[(1,-1),(0,1)]``=[(36,27,27,40,25,3,36),(27,15,5,13,13,1,27)]`

`=[(36-27,27-15,27-5,40-13,25-13,3-1,36-27),(27,15,5,13,13,1,27)]`

`=[(9,12,22,27,12,2,9),(27,15,5,13,13,1,27)]`]

Hence the original message is obtained again after encoding and decoding.