Exercise 31 Let C be the binary code with generator matrix [1 1 0 0 1 1 0] 10 101 0 1 G =|1 0 0 III0 10101 10 10 0 1011 Give another generator matrix for C that shows that C is a direct sum of two binary codes.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
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Exercise 31 Let C be the binary code with generator matrix
[1 10 0 1I0
1010101
G =|1 0 0 1110
1010110
1001011
Give another generator matrix for C that shows that C is a direct sum of two binary
codes.
Transcribed Image Text:Exercise 31 Let C be the binary code with generator matrix [1 10 0 1I0 1010101 G =|1 0 0 1110 1010110 1001011 Give another generator matrix for C that shows that C is a direct sum of two binary codes.
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