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Problem 5 (20 points) (a) Given are the matrices over Z2: G =(6819) . G2-( 1 1619). Check and explain if both matrices are generatormatrices of the same linear code. (b) Given is the checkmatrix H over Z2 of a linear code C. 0 0 0 0 0 0 01 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 01 1 1 1 H1 = 0 1 1 0 0 1 1 0 0 1 1 0 01 1 1 01010101010101 How many codewords are within C? (c) Given is the generator matrix G3 of a linear code C3 over Zs: G3 = (13) (i) Give all the codewords and the minimum distance d(C3). (ii) Give the first row of the standard-array (syndrome table) which corresponds to the codewords. In addition give one more row. Is the decoding of all the words in this second row independent from building the array (table)? Or is it depending on the way the table is build? Give an example