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Determination of (3,6) group code function e_H: B^3 --> B^6

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Coding of Binary Information and Error Detection (XIX)
Boolean Matrices

Let H = [ 1 0 0; 0 1 1; 1 1 1; 1 0 0; 0 1 0; 0 0 1 ] be a charity matrix.
Determine the (3,6) group code function e_H: B^3 --> B^6.

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