I am asked to decode this word but the concepts I've learnt tell me that the question can't be done.
Let C be a binary cyclic code generated by $g(x) = 1 + x + x^8 + x^{12} + x^{14}$ in F_2[x]/($x^{15}-1$). Assuming no more than 2 errors have occurred, decode $1 + x + x^2 + x^3 + x^6 + x^8 + x^{11} + x^{12} + x^{14}$.
Firstly, g(x) does not divide $x^{15}-1$, so g(x) does not generate a cyclic code. Secondly, even if it does, the dimension of the code would be 1, meaning there are 2 words in the code: Zero and g(x) itself.
Please correct me if my basic concepts are not right!:)