1.The generator matrix for a linear binary code is a) Express G in systematic [I[P] form. b) Determine the parity check

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1 The Generator Matrix For A Linear Binary Code Is A Express G In Systematic I P Form B Determine The Parity Check 1 (37.67 KiB) Viewed 99 times

1.The generator matrix for a linear binary code is a) Express G in systematic [I[P] form. b) Determine the parity check matrix H for the code. c) Construct the table of syndromes for the code. d) Determine the minimum distance of the code. e) Demonstrate that the code word corresponding to the information sequence 101 is orthogonal to H. 2. Consider the generator matrix in the previous problem a) Find out all the possible codewords. b) There is some relation between number of independent columns and minimum weight of the codewords. So, find out the exact relation. c) It is said that generator matrix is orthogonal to parity check matrix. Verify it. (Hint: verify if G is orthogonal to H). d) Verify if codeword space is orthogonal to that of parity-check matrix space. Verify it from any two codewords. (Hint: verify if codeword v is orthogonal to H). e) Write down the parity check equations and coding rate of the encoder. 1 0 [1 0 0 1 1 G= 0 1 0 0 1 1 1 lo 0 1 1 1 0 1