Sydnie was in group 1 and tried to decode her message by calculating the matrix (d1 ⋅ d2 ⋅ d3 ⋅ d4) and then
multiplying (d1 ⋅ d2 ⋅ d3 ⋅ d4) ⋅ c. this produced the matrix
=
10526
3
27020
3
0
24242
3
8030
30655
3
0 11336 8616 8171
−1455 −3735 0 −3351 −3330 −
8475
2
0 −4701 −3573 −
6177
2
.
a. how did she know that she made a mistake?
b. matrix c was encoded using matrices , , , and , where d1 decodes a message encoded by , d2
decodes a message encoded by , and so on. what is the relationship between matrices and d1, between
and d2, etc.?
c. the matrix that sydnie received was encoded by c = ⋅ ⋅ ⋅ ⋅ explain to sydnie how the decoding
process works to recover the original matrix and devise a correct method for decoding using multiplication
by a single decoding matrix.
d. apply the method you devised in part (c) to your group’s message to verify that it works.