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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
Finite-dimensional error-correcting code (ECC)ECC
Small-distance block code
Children
\([2^m -1, 2^m - 1 - 2m, 5]\) Melas code
\([15,6,5]\) Petersen cycle code
\((12,32,5)\) Nadler code
\((10,40,4)\) Best code
Sloane-Whitehead code
\((2^{m+1}-1,2^{2n-m},3)\) Vasilyev code
\([7,3,4]\) simplex code
\([2^m,2^m-m-1,4]\) Extended Hamming code
\([6,3,4]_4\) Hexacode
\(q\)-ary Hamming code
\([n,n-1,2]_q\) \(q\)-ary parity-check code
\([4,2,3]_4\) RS\(_4\) code
\([5,3,3]_4\) Shortened hexacode
\([11,6,5]_3\) Ternary Golay code
\([4,2,2]_{\mathbb{Z}_6}\) senary code
\((5,40,4)_{\mathbb{Z}_4}\) 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)
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Zoo Code ID: small_distance

Cite as:
“Small-distance block code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/small_distance, arXiv:2606.11484
BibTeX:
@incollection{eczoo_small_distance,
title={Small-distance block 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/small_distance}
}
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Permanent link:
https://errorcorrectionzoo.org/c/small_distance

Cite as:

“Small-distance block code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/small_distance, arXiv:2606.11484

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