A $(7,4)$ cyclic linear block code is described by the generator polinomial $g(D)=D^3+D^2+1.$

Indicate the values assumed by the "sindrome" associated to a possible single bit error, a

possible two bits error, a possible three bits error. In case of $2$ errors, how many different

sindromes are possible?

Consider the Hamming code with $N=127.$ Determine the number of possible code$-$

words, the error probability in case of both hard $($use the more precise estimation$)$ and soft

decoding, and the minimum bandwidth required to transmit $10$Mbi$\frac{t}{sec}.$