\(q\)-ary linear LCC 

Description

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

Parents

Children

Cousin

  • Multiplicity code — There exist multiplicity codes with rate arbitrarily close to one that are locally decodable and locally correctable from a constant error fraction [3].

References

[1]
Gopi, Sivakanth. Locality in coding theory. Diss. Princeton University, 2018.
[2]
S. Yekhanin, “Locally Decodable Codes”, Foundations and Trends® in Theoretical Computer Science 6, 139 (2011) DOI
[3]
S. Kopparty, S. Saraf, and S. Yekhanin, “High-rate codes with sublinear-time decoding”, Journal of the ACM 61, 1 (2014) DOI
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)— see instructions

edit on this site

Zoo Code ID: q-ary_lcc

Cite as:
\(q\)-ary linear LCC”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/q-ary_lcc
BibTeX:
@incollection{eczoo_q-ary_lcc, title={\(q\)-ary linear LCC}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/q-ary_lcc} }
Share via:
Twitter | Mastodon |  | E-mail
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.), 2023. https://errorcorrectionzoo.org/c/q-ary_lcc

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