A linear $(15,5)$ cyclic code has a generator polynomial

g$($x$)=1+$x$+$x$^(2)+$x$^(4)+$x$^(5)+$x$^(8)+$x$^(10)$

a$.$ What is the codeword length n $?$

b$.$ Determine the systematic generator matrix G$.$

c$.$ Draw the circuit diagrams for the encoder and decoder, in terms of shift registers.

d$.$ Determine the codeword for the message polynomial m$($x$)=1+$x$^(2)+$x$^(4)$

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