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 $GF(q)$)


closed as off-topic by kodlu, AleksanderRas, fkraiem, Maarten Bodewes Jul 7 at 18:06

  • This question does not appear to be about cryptography within the scope defined in the help center.
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    $\begingroup$ I'm voting to close this question as off-topic because it is a math question. $\endgroup$ – kodlu Jul 2 at 6:28
  • $\begingroup$ please consider deleting and asking at math.stackexchange $\endgroup$ – kodlu Jul 2 at 6:28
  • $\begingroup$ Even though its not directly a cryptography question, this has non-negligeable probability of being answered by a cryptographer :) $\endgroup$ – LeoDucas Jul 5 at 19:33