Fading Coder

In a finite field modulo a prime $p$, a primitive root of unity of order $n$ exists if $n$ divides $p-1$. Let $g$ be a primitive root modulo $p$. The $n$-th root of unity $\zeta_n$ is defined as: $$\zeta_n = g^{(p-1)/n} \mod p$$ Key properties analogous to complex roots of unity: $\zeta_{2n}^2 = \ze...

Polynomial Representations A polynomial $A(x) = \sum_{i=0}^{n-1} a_i x^i$ of degree $n-1$ admits two canonical representations. The coefficient representation stores the vector $[a_0, a_1, \ldots, a_{n-1}]$. Alternatively, the point-value representation consists of $n$ distinct evaluation pairs ${(x...