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Denniston code[1]

Description

Projective code that is part of a family of \([2^{a+i}+2^i-2^a,3,2^{a+i}-2^a]_{2^a}\) codes for \(i < a\) constructed using Denniston arcs [2; Sec. 19.7.3].

Notes

See corresponding MinT database entry [3].

Cousin

Member of code lists

Primary Hierarchy

Classical Domain
Galois-field Kingdom
\(q\)-ary codeECC
Additive \(q\)-ary codeECC
Linear \(q\)-ary codeECC
Projective geometry code
Projective two-weight codeLinear \(q\)-ary ECC
Parents
Projective two-weight code
Denniston codes are projective two-weight codes on maximal arcs [3][2; Sec. 19.7.3].
Griesmer codeMDS LRC Distributed-storage Linear \(q\)-ary OA Universally optimal ECC \(t\)-design
\(q\)-ary sharp configurationOA Sharp configuration Universally optimal ECC \(t\)-design
The Denniston code is a \(q\)-ary sharp configuration [4; Table 12.1].
Denniston code
Children
\([6,3,4]_4\) Hexacode
A version of the hexacode is recovered for Denniston code parameters \(i=1\) and \(a=2\) [5].

References

[1]
R. H. F. Denniston, “Some maximal arcs in finite projective planes”, Journal of Combinatorial Theory 6, 317 (1969) DOI
[2]
A. E. Brouwer, “Two-weight Codes”, Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 449-462 DOI
[3]
R. Schürer and W. Ch. Schmid, “Denniston Codes”, From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03 URL
[4]
P. Boyvalenkov, D. Danev, “Linear programming bounds”, Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 251-266 DOI
[5]
J. Bierbrauer, Introduction to Coding Theory (Chapman and Hall/CRC, 2016) DOI
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Zoo Code ID: denniston

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

Cite as:

“Denniston code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/denniston, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/projective/projective_two_weight/denniston.yml.