Lecture 38 : Guruswami - Sudan List Decoder

We now look at the list decoding algorithm in the breakthrough work of Sudan [2]. To motivate the algorithm, recall that in the previous algorithm, in order to prove that Step 2 works, we defined a polynomial R(X) △ = Q(X,P (X)). In particular, this implied that deg(R) ≤ degX(Q) + k · degY (Q) (and we had to set t > degX(Q) + k · degY (Q)). One shortcoming of this approach is that the maximum degree of X and Y might not occur at the same term. Sudan’s insight was to use a more “balanced” notion of degree of Q(X, Y ):