Hyperoval code[1]

Description

A projective code constructed using hyperovals in projective space.

Parent

Projective geometry code

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).

Cousins

\(q\)-ary sharp configuration — Codes based on hyperovals in \(PG_{2}(q)\) are \(q\)-ary sharp configurations [3; Table 12.1].
Extended GRS code — Columns of parity-check matrices of triply extended RS codes consist of points of a hyperoval [2; Prop. 17.5].

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]: W. C. Huffman, J.-L. Kim, and P. Solé, Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI

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

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