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Ta-Shma zigzag code[1]

Description

Member of a family of \(\epsilon\)-balanced codes that nearly achieves the asymptotic GV bound. The codes have relative distance \(\frac{1}{2}-\frac{\epsilon}{2}\) and rate of order \(\Omega (\epsilon^{2+\beta})\) for \(\beta\to 0\) as \(n\to\infty\) [2].

Decoding

Unique and list decoders [2].

Cousin

Member of code lists

Primary Hierarchy

Classical Domain
Binary Kingdom
Binary codeECC
Binary group-orbit codeECC
Linear binary code\(q\)-ary linear code over \(\mathbb{Z}_q\) Linear \(q\)-ary ECC
Parents
Linear binary code
Ta-Shma zigzag code

References

[1]
A. Ta-Shma, “Explicit, almost optimal, epsilon-balanced codes”, Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing (2017) DOI
[2]
F. G. Jeronimo, D. Quintana, S. Srivastava, and M. Tulsiani, “Unique Decoding of Explicit \(ε\)-balanced Codes Near the Gilbert-Varshamov Bound”, (2020) arXiv:2011.05500
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Zoo Code ID: ta-shma

Cite as:
“Ta-Shma zigzag code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/ta-shma
BibTeX:
@incollection{eczoo_ta-shma, title={Ta-Shma zigzag code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/ta-shma} }
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Permanent link:
https://errorcorrectionzoo.org/c/ta-shma

Cite as:

“Ta-Shma zigzag code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/ta-shma

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/bits/ta-shma.yml.