Let C be a cyclic (n,k) code with generator g. We present a way to estimate how good the cyclic code generated by g is.

Naturally, it is important to be able to find the information vector corresponding to a code word. For this, the check polynomial h = (Xn-1)/g is used.

Cyclic decoding theorem

If c is a code word, viewed as a polynomial of degree at most n-1, then the information vector corresponding to the code word c is the element of minimal degree in ch+(Xn).