  In this paper, we first propose a general interpolation algorithm in a free
module of a linearized polynomial ring, and then apply this algorithm to decode
several important families of codes, Gabidulin codes, KK codes and MV codes.
Our decoding algorithm for Gabidulin codes is different from the polynomial
reconstruction algorithm by Loidreau. When applied to decode KK codes, our
interpolation algorithm is equivalent to the Sudan-style list-1 decoding
algorithm proposed by K/"otter and Kschischang for KK codes. The general
interpolation approach is also capable of solving the interpolation problem for
the list decoding of MV codes proposed by Mahdavifar and Vardy, and has a lower
complexity than solving linear equations.
