$ C $ is a $ q $– conical cyclic $ (n, k) $-code where $ (n, q) = 1 $, with polynomial generator $ g (X) $. Show that $ (1,1, cdots, 1) en C Leftrightarrow X-1 nmid g (X) $.

I don't know if I'm right:

$ x ^ n -1 = (x – 1) (1 + x + x2 cdots + x ^ n-1) $.

As $ g (x) $ it is a generator polynomial so it divides $ x ^ n −1 $ and he has not $ x – $ 1 as a factor, you must divide $ 1 + x + x 2 cdots + x ^ n-1 $. In other words, the length n word consisting of all $ 1 $& # 39; s is a code word