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Question
Using encoding matrix `[(1,1),(0,1)]`encode and decode the message
“ALL IS WELL” .
Sum
Solution
Let encoding matix A = `[(1,1),(0,1)]`
The message is ALL IS WELL and Let B is the matrix in number form,
`B=[(1,12,9,0,5,12),(12,0,19,23,12,0)]`
`"A.B"=[(1,1),(0,1)][(1,12,9,0,5,12),(12,0,19,23,12,0)]`
`"C"=[(13,12,28,23,17,12),(12,0,19,23,12,0)]`
The encoded message is given by,
13 12 12 0 28 19 23 23 17 12 12 0
“MLL ASWWQLL “
Inverse of encoding matix A = `[(1,1),(0,1)]` is given by ,
`A^(-1)=[(1,-1),(0,1)][(13,12,28,23,17,12),(12,0,19,23,12,0)]`
Decoded matrix is given by ,
`"B"=A^(-1)."C"=[(1,-1),(0,1)][(13,12,28,23,17,12),(12,0,19,23,12,0)]`
`B=[(1,12,9,0,5,12),(12,0,19,23,12,0)]`
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Application of Inverse of a Matrix to Coding Theory
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