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How do you show that a given encoding functione:B^3 --> B^7 is a group code?

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Coding of Binary Information and Error Detection (XI)
Group Code of an Encoding Function

Show that the (3, 7) encoding function e: B^3 --> B^7 defined by

e(000) = 0000000
e(001) = 0010110
e(010) = 0101000
e(011) = 0111110
e(100) = 1000101
e(101) = 1010011
e(110) = 1101101
e(111) = 1111011

is a group code.

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Solution Summary

This solution shows how the encoding function e:B^3 --> B^7 is a group code. The solution is presented in an attached Word document.

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