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\(q\)-ary linear LCC

Description

A \(q\)-ary linear code for which one can recover any coordinate of a codeword from at most \(r\) coordinates of a received word (assuming the corruption rate is within some tolerated threshold \(\delta\)).

Cousins

Member of code lists

Primary Hierarchy

Classical Domain
Galois-field Kingdom
\(q\)-ary codeECC
Additive \(q\)-ary codeECC
Linear \(q\)-ary codeECC
Parents
Linear \(q\)-ary code
Locally correctable code (LCC)LRC Distributed-storage ECC
\(q\)-ary linear LCC
Children
\([2^m,m,2^{m-1}]\) Hadamard code
Hadamard codes are two-query LDCs and LCCs [1,3].
Generalized RM (GRM) code
GRM codes are LDCs and LCCs [1,3].

References

[1]
S. Gopi, “Locality in coding theory”, PhD thesis, Princeton University, 2018.
[2]
S. Kopparty, S. Saraf, and S. Yekhanin, “High-rate codes with sublinear-time decoding”, Journal of the ACM 61, 1 (2014) DOI
[3]
S. Yekhanin, “Locally Decodable Codes”, Foundations and Trends® in Theoretical Computer Science 6, 139 (2012) DOI
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Zoo Code ID: q-ary_lcc

Cite as:
“\(q\)-ary linear LCC”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/q-ary_lcc, arXiv:2606.11484
BibTeX:
@incollection{eczoo_q-ary_lcc,
title={\(q\)-ary linear LCC},
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/q-ary_lcc}
}
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Permanent link:
https://errorcorrectionzoo.org/c/q-ary_lcc

Cite as:

“\(q\)-ary linear LCC”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/q-ary_lcc, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/distributed_storage/q-ary_lcc.yml.