Assign a number to each letter of the alphabet (with O assigned to a blank space),...
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Assign a number to each letter of the alphabet (with O assigned to a blank space), as shown. 1 = A 2= B 3=C 4= D 5=E 6 = F - G 8 = H 9=1 10 = J 11 = K 12 = L 13 = M 14 = N 150 16 P 17 = Q 18 = R 19 = S 20 T 21 U 22 = V 23 W 24= X 25 Y 26 -Z Then convert the message to numbers and partition it into uncoded row matrices, each having n entries, as demonstrated in Example 1. EXAMPLE 1 Write the uncoded row matrices of size 1 x 3 for the message MEET ME MONDAY. SOLUTION Partitioning the message (including blank spaces, but ignoring punctuation) into groups of three produces the uncoded row matrices shown below. [13 5 5] [20 0 13] [5 0 13] [15 14 4] [1 25 0] MEET MO NDAY ME Note the use of a blank space to fill out the last uncoded row matrix. To encode the message, choose an n x n invertible matrix A and multiply the uncoded row matrices (on the right) by A to obtain coded row matrices. Example 2 demonstrates this process. Study the "Matrix Encoding Method" described below. Then develop an algorithm to decode messages obtained using the "Encoding Method." Describe your decoding algorithm. Assign a number to each letter of the alphabet (with O assigned to a blank space), as shown. 1 = A 2= B 3=C 4= D 5=E 6 = F - G 8 = H 9=1 10 = J 11 = K 12 = L 13 = M 14 = N 150 16 P 17 = Q 18 = R 19 = S 20 T 21 U 22 = V 23 W 24= X 25 Y 26 -Z Then convert the message to numbers and partition it into uncoded row matrices, each having n entries, as demonstrated in Example 1. EXAMPLE 1 Write the uncoded row matrices of size 1 x 3 for the message MEET ME MONDAY. SOLUTION Partitioning the message (including blank spaces, but ignoring punctuation) into groups of three produces the uncoded row matrices shown below. [13 5 5] [20 0 13] [5 0 13] [15 14 4] [1 25 0] MEET MO NDAY ME Note the use of a blank space to fill out the last uncoded row matrix. To encode the message, choose an n x n invertible matrix A and multiply the uncoded row matrices (on the right) by A to obtain coded row matrices. Example 2 demonstrates this process. Study the "Matrix Encoding Method" described below. Then develop an algorithm to decode messages obtained using the "Encoding Method." Describe your decoding algorithm.
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Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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