Tensored-Ramanujan-complex product code[1]
Description
Code constructed in a similar way as the Ramanujan-complex product code, but utilizing tensor products of Ramanujan complexes in order to improve code distance from \(\sqrt{n}\log n\) to \(\sqrt{n}~\text{polylog}(n)\). The utility of such tensor products comes from the fact that one of the Ramanujan complexes is a collective cosystolic expander as opposed to just a cosystolic expander.
Protection
Construction yields explicit QLDPC codes with distance \(\sqrt{n}\log^c n\) using the \(c\)-tensor-product of Ramanujan complexes.
Parent
References
- [1]
- T. Kaufman and R. J. Tessler, “New Cosystolic Expanders from Tensors Imply Explicit Quantum LDPC Codes with \(Ω(\sqrt{n}\log^kn)\) Distance”, (2020) arXiv:2008.09495
Page edit log
- Victor V. Albert (2022-10-02) — most recent
Cite as:
“Tensored-Ramanujan-complex product code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/iterated_ramanujan