Note on majority-logic decoding of finite geometry codes (Corresp.)

In a recent paper [1], techniques for reducing the number of majority-logic decoding steps for finite geometry codes have been proposed. However, the lower bound of [1, lemma 4] is incorrect; finite geometry codes, in general, cannot be decoded in less than or equal to three steps of orthogonalization, as was claimed. This correspondence presents a decoding procedure for finite geometry codes that requires as few decoding steps as possible. It is shown that the minimum number of steps is a logarithmic function of the dimension of the associated geometry.