According to Google Scholar original Gallager's article [Low-density parity-check codes](http://ieeexplore.ieee.org/document/1057683/) is cited more than 10000 times. It looks scary for non-experts.


I suspect that the number of algorithms for constructing good sparse matrices for [LDPC-codes](https://en.wikipedia.org/wiki/Low-density_parity-check_code) is much less than 10000. Is there any survey which contains description of such algorithms? 


Basically I'm interested in explicit constructions based on number theory methods.



LDPC codes construction
[Ryan and Lin's *Channel Codes*](https://books.google.com/books?id=0gwqxBU_t-QC) has several chapters (computer-based, finite geometries, finite fields, combinatorial designs) devoted to various constructions of LDPC codes, as well as a chapter devoted to nonbinary codes that also details constructions for that case.


