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Ben-Sasson-Goldreich-Harsha-Sudan-Vadhan (BGHSV) code[1]

Description

A member of a family of locally testable \([n,k,d]\) codes with \(n = k^{1+\epsilon}\) and query complexity of order \(O(1/\epsilon)\), for any fixed \(\epsilon > 0\).

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
Binary linear LTCLinear \(q\)-ary LTC ECC
Parents
Binary linear LTC
Ben-Sasson-Goldreich-Harsha-Sudan-Vadhan (BGHSV) code

References

[1]
E. Ben-Sasson, O. Goldreich, P. Harsha, M. Sudan, and S. Vadhan, “Robust pcps of proximity, shorter pcps and applications to coding”, Proceedings of the thirty-sixth annual ACM symposium on Theory of computing 1 (2004) DOI
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Your contribution is welcome!

on github.com (edit & pull request)

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Zoo Code ID: bsghsv-ltc

Cite as:
“Ben-Sasson-Goldreich-Harsha-Sudan-Vadhan (BGHSV) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/bsghsv-ltc, arXiv:2606.11484
BibTeX:
@incollection{eczoo_bsghsv-ltc,
title={Ben-Sasson-Goldreich-Harsha-Sudan-Vadhan (BGHSV) 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/bsghsv-ltc}
}
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Permanent link:
https://errorcorrectionzoo.org/c/bsghsv-ltc

Cite as:

“Ben-Sasson-Goldreich-Harsha-Sudan-Vadhan (BGHSV) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/bsghsv-ltc, arXiv:2606.11484

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