Denniston code

Denniston code[1]

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.

See corresponding MinT database entry [2].

Projective two-weight code — Denniston codes are projective two-weight codes on maximal arcs [2][3; Sec. 19.7.3].
Griesmer code
\(q\)-ary sharp configuration — The Denniston code is a \(q\)-ary sharp configuration [4; Table 12.1].

Hexacode — A version of the hexacode is recovered for Dennison code parameters \(i=1\) and \(a=2\) [5].

Hyperoval code — Denniston codes for \(i=1\) are based on hyperovals in \(PG(2,2^a)\) [2].

[1]: R. H. F. Denniston, “Some maximal arcs in finite projective planes”, Journal of Combinatorial Theory 6, 317 (1969) DOI
[2]: Rudolf Schürer and Wolfgang Ch. Schmid. “Denniston Codes.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. https://mint.sbg.ac.at/desc_CDenniston.html
[3]: A. E. Brouwer, "Two-weight Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
[4]: P. Boyvalenkov, D. Danev, "Linear programming bounds." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
[5]: J. Bierbrauer, Introduction to Coding Theory (Chapman and Hall/CRC, 2016) DOI

Page edit log

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