Generally, low density parity codes are decoded using sum product decoder (also known as decoding under belief propagation). Such codes are usually decoded nicely if there are no short length cycles in tanner graph, in particular length 4 cycles are to be avoided. Naturally, this puts some bound on column weight in such a parity matrix. What is the general column weight $t$ that is allowed (in terms of code dimensions $k,n$) so that there are no 4-cycles?
To state it formally
given n and k what is maximum value of $t$ for which tanner graph (bipartite t regular) has no 4 cycle?