[Jump to code hierarchy]

Small-distance block code

Description

A block code of length \(n\) that either detects or corrects errors on at most two coordinates, i.e., has distance \(d \leq 5\).

See Ref. [1] for a comparison of short block codes.

Cousins

Member of code lists

Primary Hierarchy

Classical Domain
Error-correcting code (ECC)
Block code
Parents
Block code
Small-distance block code
Children
Melas code
\([7,3,4]\) simplex code
\([2^r,2^r-r-1,4]\) Extended Hamming code
Petersen cycle code
Preparata code
Nadler code
\((10,40,4)\) Best code
Sloane-Whitehead code
Vasilyev code
Hexacode
\(q\)-ary Hamming code
\(q\)-ary parity-check code
Ternary Golay code
Pentacode

References

[1]
M. C. Coşkun, G. Durisi, T. Jerkovits, G. Liva, W. Ryan, B. Stein, and F. Steiner, “Efficient Error-Correcting Codes in the Short Blocklength Regime”, (2019) arXiv:1812.08562
[2]
F. J. MacWilliams and N. J. A. Sloane. The theory of error correcting codes. Elsevier, 1977.
Page edit log

Your contribution is welcome!

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

edit on this site

Zoo Code ID: small_distance

Cite as:
“Small-distance block code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/small_distance
BibTeX:
@incollection{eczoo_small_distance, title={Small-distance block code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/small_distance} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/small_distance

Cite as:

“Small-distance block code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/small_distance

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/properties/block/small_distance.yml.