Let fc : M represent the channel coding map, where M is the set of message words

Question

Let fc : M represent the channel coding map, where M is the set of message words and C is the set of code words. For a linear block code, fe, one can obtain a matrix representation of fe which has the form (note that, with some abuse of notation, we are using fe to represent both the code and it's matrix representation) where I is the identify matrix and op computes the parity bits. All the entries are in F2. The parity check matrix may then be computed as Note that 1-0. Specify the matrix Op for a (15,11) hanning code.

Explanation / Answer

n = 15, k = 11, d = n - k = 4

Columns are generated using linearly independent tuples.

Phi_p =

1 0 1 1 1 0 0 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 1 1 0 0 1 0

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