I have been reading a paper that states that a generator polynomial
$$ G(D)= 1+ D^4+D^7$$ creates a 127 bit sequence which is as follows
00001110 11110010 11001001 00000010 00100110 00101110 10110110 00001100 11010100 11100111 10110100 00101010 11111010 01010001 10111000 1111111
if the initial state used is 1111111.
I don't understand why this is the case
My thoughts are as follows:
$G(D)= 1+ D^4+D^7 $----> in time domain is equivalent to $1 0 0 0 1 0 0 1$. How can I use the initial state to generate the 127 bit sequence. DO I perform a convolution between two sequences?
Thanks in advance for any help.