Binned orthogonal/bi-orthogonal codes have been proposed as dirty-paper codes for digital watermarking due to its simplicity in both encoding and decoding, robustness against volumetric scaling, and performance gain over conventional non-dirty paper coded systems. In this paper, we extend the binned orthogonal/bi-orthogonal code to generalized binned linear binary code, and propose an efficient binning method to achieve good coding performance. We also derive a closed-form expression for its BER performance in dirty paper watermarking systems. Simulations show that the derived BER formula is very tight. The binned linear binary codes offer much higher code rates, hence significant coding gains, over its orthogonal/bi-orthogonal counterparts. This translates into improved invisibility for the hidden data and better perceptual quality for the watermarked image for a given robustness requirement for the hidden data.