4. The factor (1 + x) always divides x +1 without a remainder, therefore, g(x) =...

   

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4. The factor (1 + x) always divides x" +1 without a remainder, therefore, g(x) = 1 + x can be a generator polynomial for a binary cyclic code of length n with k information bits. a. First show that g(x) is a factor of x" + 1 for any n. b. Express k, the number of information bits in terms of n, the codeword's overall length, in other words this is an (n,k) code where k is expressed in terms of n. c. Can you determine the dmin for this code? How many errors will this code correct? detect? d. Can you describe in words what this code is? e. Draw the diagram of the (n-k) stage encoding circuit, then choose any valid information sequence and calculate the remainder using the encoder circuit. Does this help to answer part d. for this problem? 4. The factor (1 + x) always divides x" +1 without a remainder, therefore, g(x) = 1 + x can be a generator polynomial for a binary cyclic code of length n with k information bits. a. First show that g(x) is a factor of x" + 1 for any n. b. Express k, the number of information bits in terms of n, the codeword's overall length, in other words this is an (n,k) code where k is expressed in terms of n. c. Can you determine the dmin for this code? How many errors will this code correct? detect? d. Can you describe in words what this code is? e. Draw the diagram of the (n-k) stage encoding circuit, then choose any valid information sequence and calculate the remainder using the encoder circuit. Does this help to answer part d. for this problem?