Hyperoval code[1]
Description
A projective code constructed using hyperovals in projective space.
Parent
Child
- Hexacode — Columns of hexacode's generator matrix represent the six homogeneous coordinates of a hyperoval in the projective plane \(PG(2,4)\) [2; pg. 289][3; Exam. 19.2.1].
Cousins
- \(q\)-ary sharp configuration — Codes based on hyperovals in \(PG_{2}(q)\) are \(q\)-ary sharp configurations [4; Table 12.1].
- Projective two-weight code — Codes based on hyperovals in \(PG_{2}(q)\) with even \(q\) are projective two-weight codes [3; Exam. 19.2.1].
- Extended GRS code — Columns of parity-check matrices of triply extended RS codes consist of points of a hyperoval [2; Prop. 17.5].
- Denniston code — Denniston codes for \(i=1\) are based on hyperovals in \(PG(2,2^a)\) [5].
References
- [1]
- R. C. Bose (1947). Mathematical theory of the symmetrical factorial design. Sankhyā: The Indian Journal of Statistics, 107-166.
- [2]
- J. Bierbrauer, Introduction to Coding Theory (Chapman and Hall/CRC, 2016) DOI
- [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]
- Rudolf Schürer and Wolfgang Ch. Schmid. “Denniston Codes.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. http://mint.sbg.ac.at/desc_CDenniston.html
Page edit log
- Victor V. Albert (2023-03-05) — most recent
- Alexander Barg (2023-03-05)
- Victor V. Albert (2023-02-24)
Cite as:
“Hyperoval code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/hyperoval