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Lazebnik-Ustimenko (LU) code[1,2]

Description

LDPC code whose Tanner graph comes from a particular family of \(q\)-regular graphs [1] of known girth and relatively large stopping sets.

Member of code lists

Primary Hierarchy

Classical Domain
Binary Kingdom
Binary codeECC
Binary group-orbit codeECC
Linear binary codeLinear \(q\)-ary Linear code over \(\mathbb{Z}_q\) ECC
Low-density parity-check (LDPC) code\(q\)-ary LDPC Tanner Linear \(q\)-ary LRC Distributed-storage ECC
Regular LDPC codeTanner Linear \(q\)-ary Linear code over \(\mathbb{Z}_q\) ECC
Parents
Regular LDPC code
Algebraic LDPC code\(q\)-ary LDPC Tanner Linear \(q\)-ary Linear code over \(\mathbb{Z}_q\) LRC Distributed-storage ECC
Lazebnik-Ustimenko (LU) code

References

[1]
F. Lazebnik and V. A. Ustimenko, “Explicit construction of graphs with an arbitrary large girth and of large size”, Discrete Applied Mathematics 60, 275 (1995) DOI
[2]
J.-L. Kim, U. N. Peled, I. Perepelitsa, V. Pless, and S. Friedland, “Explicit Construction of Families of LDPC Codes With No<tex>\(4\)</tex>-Cycles”, IEEE Transactions on Information Theory 50, 2378 (2004) DOI
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Zoo Code ID: lu_ldpc

Cite as:
“Lazebnik-Ustimenko (LU) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/lu_ldpc, arXiv:2606.11484
BibTeX:
@incollection{eczoo_lu_ldpc,
title={Lazebnik-Ustimenko (LU) code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/lu_ldpc}
}
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Permanent link:
https://errorcorrectionzoo.org/c/lu_ldpc

Cite as:

“Lazebnik-Ustimenko (LU) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/lu_ldpc, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/bits/tanner/regular_tanner/regular_ldpc/lu_ldpc.yml.