We study a class of finite geometry codes referred to as finite hyperplane codes, which are constructed based on hyperplanes and flats of a lower dimension in a finite geometry over the finite field F 2 s. We will determine the minimum distance for this class of codes and reveal a special property of them. In particular, we will show that for a finite geometry code based on flats of two non-consecutive dimensions, the error-correction capability guaranteed by Rudolph's one-step majority-logic decoding algorithm is less than or equal to that guaranteed by Reed-Massey's multi-step majority-logic decoding algorithm, with equality if and only if the code is a finite hyperplane code. In addition, both decoding algorithms can achieve the error-correction capability of finite hyperplane codes.