# Constructing Low-Density Parity-Check Codes of length $n$ and minimum distance = $\delta n$ over $GF(q)$? [closed]

I am looking for a way to construct an LDPC (Low-Density Parity-Check) Code $$C$$ of length $$n$$ and minimum distance $$d_C$$ that scales linearly to $$n$$, meaning $$d_C = \delta n$$ for $$\delta \in (0,1)$$.

I have been looking through the state-of-the-art papers about the construction of LDPC Codes, and seeing their minimum distance. Some codes are quasi-cylic (QC-LDPC) and cylic (C-LDPC), and are supposed to have "good" minimum distance, but they only scale to $$\sqrt n$$ at most.

Some papers efficiently construct such codes, but with the case over $$GF(q)$$ where $$q = 2^m$$, like Tanner Codes and Distance amplification for example.

Some other papers state, or even try to prove theoretically that such codes with $$d_C = \delta n$$ can be found, but dont' provide any partical way for the construction (for example), and don't reference any other papers for such constructions.

So I ask this question after a lot of research : is there any efficient algorithm to construct LDPC codes $$C$$ of length $$n$$ and minimum distance that scales linearly to the length $$d_C = \delta n$$ (over any $$GF(q)$$)

• I'm voting to close this question as off-topic because it is a math question. – kodlu Jul 2 '19 at 6:28
• please consider deleting and asking at math.stackexchange – kodlu Jul 2 '19 at 6:28
• Even though its not directly a cryptography question, this has non-negligeable probability of being answered by a cryptographer :) – LeoDucas Jul 5 '19 at 19:33