Which Codes Have 4-Cycle-Free Tanner Graphs?

Abstract

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