Here is a list of LDPC codes.
Code Description
Low-density parity-check (LDPC) code Also known as Gallager codes. Binary or $$q$$-ary linear code with a sparse parity-check matrix. More precisely, a member of an infinite family of $$[n,k,d]$$ codes for which the number of nonzero entries in each row and column of the parity-check matrix are both bounded by a constant as $$n\to\infty$$. An LDPC code is $$(j,k)$$-regular if the parity-check matrix has a fixed number of $$j$$ nonzero entries in each row and $$k$$ entries in each column; otherwise, the LDPC code is irregular. The dual of an LDPC code has a sparse generator matrix and is called an LDGM code.