Here is a list of good QLDPC and related codes.

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Code Relation
Dinur-Hsieh-Lin-Vidick (DHLV) code DHLV code construction yields asymptotically good QLDPC codes.
Expander LP code Lifted products of certain classical Tanner codes are the first asymptotically good QLDPC codes.
Lattice stabilizer code Chain complexes describing some QLDPC codes [1,2], and, more generally, CSS codes [3] can be ‘lifted’ into higher-dimensional manifolds admitting some notion of geometric locality. Applying this procedure to good QLDPC codes yields \([[n,n^{1-2/D},n^{1-1/D}]]\) lattice stabilizer codes in \(D\) spatial dimensions that saturate the BPT bound [2,4,5].
Lattice subsystem code An \([[n,k,d]]\) qubit stabilizer code can be converted into an order \([[O(\ell \delta n),k,\Omega(d/w)]]\) subsystem qubit stabilizer code with weight-three gauge operators via the wire-code mapping [6], which uses weight reduction. Here, \(w\) and \(\delta\) are the weight and degree of the input code’s Tanner graph, while \(\ell\) is the length of the longest edge of a particular embedding of that graph. Applying this procedure to good QLDPC codes and using an embedding into \(D\)-dimensional Euclidean space yields lattice subsystem codes whose logical-qubit number and distance both scale as \(\Theta(n^{1-1/D})\) as functions of block length \(n\), saturating the subsystem BT bound [6].
Layer code Layer code parameters, of order \((10,40,4)\), achieve the BPT bound in 3D when asymptotically good QLDPC codes are used in the construction.
Lossless expander balanced-product code Taking a balanced product of two-sided expanders, which are only conjectured to exist, yields an asymptotically good QLDPC code family [7].
Quantum Tanner code Quantum Tanner code construction yields asymptotically good QLDPC codes.
Quantum maximum-distance-separable (MDS) code AEL distance amplification [8,9] can be used to construct asymptotically good QLDPC codes that approach the quantum Singleton bound [10; Corr. 5.3].
Singleton-bound approaching AQECC The AEL distance-amplification framework also yields constant-alphabet approximate quantum codes that decode nearly up to the quantum Singleton bound [10].

References

[1]
M. Freedman and M. B. Hastings, “Building manifolds from quantum codes”, (2021) arXiv:2012.02249
[2]
T.-C. Lin, A. Wills, and M.-H. Hsieh, “Geometrically Local Quantum and Classical Codes from Subdivision”, (2024) arXiv:2309.16104
[3]
V. Guemard, “Lifts of quantum CSS codes”, (2024) arXiv:2404.16736
[4]
E. Portnoy, “Local Quantum Codes from Subdivided Manifolds”, (2023) arXiv:2303.06755
[5]
X. Li, T.-C. Lin, and M.-H. Hsieh, “Transform Arbitrary Good Quantum LDPC Codes into Good Geometrically Local Codes in Any Dimension”, (2024) arXiv:2408.01769
[6]
N. Baspin and D. Williamson, “Wire Codes”, (2024) arXiv:2410.10194
[7]
T.-C. Lin and M.-H. Hsieh, “Good quantum LDPC codes with linear time decoder from lossless expanders”, (2022) arXiv:2203.03581
[8]
N. Alon, J. Edmonds, and M. Luby, “Linear time erasure codes with nearly optimal recovery”, Proceedings of IEEE 36th Annual Foundations of Computer Science 512 DOI
[9]
N. Alon and M. Luby, “A linear time erasure-resilient code with nearly optimal recovery”, IEEE Transactions on Information Theory 42, 1732 (1996) DOI
[10]
T. Bergamaschi, L. Golowich, and S. Gunn, “Approaching the Quantum Singleton Bound with Approximate Error Correction”, (2022) arXiv:2212.09935