The LFSR sequence

$10111001$

is generated by a recurrence of

length $3$:

xn$+3$ c$0$xn $+$ c$1$xn$+1+$ c$2$xn$+2($mod $2).$ Find the coefficients c$0,$c$1,$ and c$2.$

Solve problem by hand in each case showing work for the following steps:

the parameter m for the length of the recursion

the m x m linear system used to solve for the coefficients

the coefficients and recursion equation

however many of the next terms of the series which are asked for