Polynomial multiplication parity-check matrix

A binary check polynomial $h={\sum }_{j=0}^{N-1}{h}_j{X}^j$ modulo $X^N+1$ gives the circulant matrix $B_{ti}=h_{t-i\mathrm{mod}N}$ representing multiplication by $h$. Its kernel is the cyclic code. Selecting independent rows gives a parity-check matrix of rank equal to the redundancy, even when the supplied polynomial is not the canonical check polynomial.

// Target: algebra.bigb