Binary cyclic codes of length a power of two

For $N=2^t$, the binary cyclic codes are exactly the nested ideals generated by $(X+1{)}^j$ for $0\le j\le N$. They have dimensions $N-j$ and canonical check polynomials $(X+1{)}^{N-j}$. The endpoint ideals are the entire word space and the zero code.

// Target: algebra.bigb