Many different LDPC code constructions exist for almost any possible application. However, finding good LDPC Codes is not an easy task. Especially for finite length codes many different techniques have been presented in the last decades. All these code constructions need to be verified by bit-error-rate simulations, since the decoding behavior cannot be fully predicted by theoretical approaches.

The Institute of Telecommunications (INUE) provides several webdemos for creating low-density parity-check (LDPC) codes, which are usually defined by their parity-check matrix $\mathbf{H}$. See the following webdemos for a detailed explanation:

Webdemo - Degree Distribution Optimization

Webdemo - LDPC Codes from Communication Standards

Webdemo - Spatially Coupled LDPC Codes

You can download the codes from these webdemos and upload them in this webdemo in order to see the real bit-error-rate performance after a few seconds.

Or you can simply upload your own arbitrary $\mathbf{H}$ matrix for a quick online simulation.