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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 $GF(q)$)

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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.
If this question can be reworded to fit the rules in the help center, please edit the question.

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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