Consider the generator polynomial for a (15, 11) cyclic code defined by g(p) = p^4 + p + 1 a) Assume that the generator polynomial is directly used to encode the input information bits to obtain the codeword as c(p) = m(p)g(p), where c(p) is the codeword polynomial and m(p) is theinput information polynomial. Find the first three rows of the equivalent generator matrix forthe encoder. You don’t need to present the entire generator matrix, just the first three rows aresufficient. b) Still assume that the generator polynomial is directly used to encode the input information bits toobtain the codeword. How many bit errors in the codeword can this code correct? c) Now assume that the encoder is required to produce systematic codewords using the generator polynomial. Find the first three rows of the equivalent generator matrix for the systematic encoder.You don’t need to present the entire generator matrix, just the first three rows are sufficient.
Consider the generator polynomial for a (15, 11) cyclic code defined by
g(p) = p^4 + p + 1
a) Assume that the generator polynomial is directly used to encode the input information bits to obtain the codeword as c(p) = m(p)g(p), where c(p) is the codeword polynomial and m(p) is the
input information polynomial. Find the first three rows of the equivalent generator matrix for
the encoder. You don’t need to present the entire generator matrix, just the first three rows are
sufficient.
b) Still assume that the generator polynomial is directly used to encode the input information bits to
obtain the codeword. How many bit errors in the codeword can this code correct?
c) Now assume that the encoder is required to produce systematic codewords using the generator polynomial. Find the first three rows of the equivalent generator matrix for the systematic encoder.
You don’t need to present the entire generator matrix, just the first three rows are sufficient.
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