Let C be an [n,k,d] binary linear code with rate R=k/n and dual C perp. In this correspondence, it is shown that C can be represented by a 4-cycle-free Tanner graph only if: pdperples lfloorradicnp(p-1)+n2/4+n/2 rfloorwhere p=n-k and dperp is the minimum distance of C perp. By applying this result, it is shown that 4-cycle- free Tanner graphs do not exist for many classical binary linear block codes