Develop the encoder and syndrome calculator with 1+x² + x³ as generator polynomial in Problem P4.18.

In Problem

Polynomial 1 + x⁷ can be factorized into three irreducible polynomials (1 + x)(1 + x + x³)(1 + x² + x³) with (1 + x + x³) and (1 + x² + x³) as primitive polynomials. Using 1 + x + x³ as generator polynomial, calculate the (7, 4) cyclic code word for given message sequence 1010.