Two classes of LDPC codes from the space of hermitian matrices over finite fields
Meng Zhao, Changli Ma, Yanan Feng, Qi Wang · Advances in Mathematics of Communications · 2022
For a prime power \begin{document}$ q $\end{document} , we construct two classes of LDPC codes \begin{document}$ C(n, q^2) $\end{document} and \begin{document}$ C^T(n, q^2) $\end{document} , both with girth \begin{document}$ 8 $\end{document} , based on the space of \begin{document}$ n\times n $\end{document} Hermitian matrices over the finite field \begin{document}$ \mathbb{F}_{q^2} $\end{document} . The minimum distance and the stopping distance are both determined for \begin{document}$ C^T(n, q^2) $\end{document} . Meanwhile, lower bounds of these parameters are obtained for \begin{document}$ C(n, q^2) $\end{document} . Furthermore, when the characteristic of \begin{document}$ \mathbb{F}_{q^2} $\end{document} is \begin{document}$ 2 $\end{document} , we are also able to derive upper bounds of these two parameters for \begin{document}$ C(n, q^2) $\end{document} .