Develop the encoder and syndrome calculator with 1 x 2 x 3 as generator polynomial in Problem P4 18 In Problem Polynomial 1 x 7 can be factorized into three irreducible polynomials (1 x)(1 x x 3 )(1 x 2 x 3 ) with (1 x x 3 ) and (1 x 2 x 3 ) as primitive polynomials Using 1 x x 3 as generator polyn...

Encoder for the 7 4 cyclic code genera ...

Develop the encoder and syndrome calculator with 1+x 2 + x 3 as generator polynomial in Problem

Question:

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.