Application

We use the map to convert an information vector from (Z/2Z)^k into a code word in C. This is done as follows:

Let a = (a₀, ... ,a _k-1) be a vector in (Z/2Z)^k.

Form the polynomal a = a₀ + a₁X + ··· + a_k-1X^k-1.

Compute ag mod (Xⁿ-1) = c₀ + c₁X + ··· + c_{n - 1}X^{n - 1}.

This corresponds to the code word c = (c₀, ... , c_{n - 1}). Thus, the information vector a is transformed into the code word c.