A Recursive Formula for Power Moments of 2-Dimensional Kloosterman Sums Assiciated with General Linear Groups

In this paper, we construct a binary linear code connected with the Kloosterman sum for $GL(2,q)$. Here $q$ is a power of two. Then we obtain a recursive formula generating the power moments 2-dimensional Kloosterman sum, equivalently that generating the even power moments of Kloosterman sum in terms of the frequencies of weights in the code. This is done via Pless power moment identity and by utilizing the explicit expression of the Kloosterman sum for $GL(2,q)$.