I've got $\alpha$ as a primitive element of $F_{2^4}$ satisfying $\alpha^4 + \alpha + 1 = 0$ and the [15,7,5] binary BCH code given by the generator polynomial $g(x) = x^8 +x^7+x^6+x^4+1 = \prod_{i \in C_i \cup C_3} (x-\alpha^i)$.
(Where $C_j$ is the cyclotomic coset containing j.)
A vector R = (1,0,0,1,1,0,0,1,1,0,1,0,1,1,0) is recieved.
How can I now compute the syndromes of R?
Thanks for any help!
Take $R$ as a polynomial and divide it by $g(x)$. The residue gives the syndrome.