Denniston code[1]

Description

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

Parents

Projective geometry code — Columns of Denniston code generator matrices represent points of a Denniston arc.
Griesmer code
\(q\)-ary sharp configuration — The Denniston code is a \(q\)-ary sharp configuration [2; Table 12.1].

Child

Hexacode — A version of the hexacode is recovered for Dennison code parameters \(i=1\) and \(a=2\) [3].

References

[1]: R. H. F. Denniston, “Some maximal arcs in finite projective planes”, Journal of Combinatorial Theory 6, 317 (1969) DOI
[2]: W. C. Huffman, J.-L. Kim, and P. Solé, Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
[3]: J. Bierbrauer, Introduction to Coding Theory (Chapman and Hall/CRC, 2016) DOI

Page edit log

Victor V. Albert (2022-08-09) — most recent

Cite as:

“Denniston code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/denniston

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