3. (a) consider the following two codewords 1010011 0011101 First write them as polynomials and then find an expression that can be used to produce a cyclic shift of that codeword by one bit position using polynomial multiplication (Hint: you will need a different multiplier expression for each of the codewords above). Suggest a simple test that could be used on ANY codeword to determine which of your expressions should be used for the polynomial multiplication. (b) what is the Hamming weight of each of the codewords used for (a) and what is the Hamming distance between them ? (c) State the criteria for a Hamming code and check the codewords used for (a) to determine if they could belong to a Hamming code 4. A rate 1/3 convolutional code is described by the generator transfer-function matrix G(D= (1 +D 1+D+D2 1+D?] (a) Draw a diagram of the encoder and indicate the shift registers that represent the state of the encoder (b) Determine the State Table for this code (c) Draw the State Diagram 3. (a) consider the following two codewords 1010011 0011101 First write them as polynomials and then find an expression that can be used to produce a cyclic shift of that codeword by one bit position using polynomial multiplication (Hint: you will need a different multiplier expression for each of the codewords above). Suggest a simple test that could be used on ANY codeword to determine which of your expressions should be used for the polynomial multiplication. (b) what is the Hamming weight of each of the codewords used for (a) and what is the Hamming distance between them ? (c) State the criteria for a Hamming code and check the codewords used for (a) to determine if they could belong to a Hamming code 4. A rate 1/3 convolutional code is described by the generator transfer-function matrix G(D= (1 +D 1+D+D2 1+D?] (a) Draw a diagram of the encoder and indicate the shift registers that represent the state of the encoder (b) Determine the State Table for this code (c) Draw the State Diagram