Description
Member of a \([q^2+1,4,q^2-q]_q\) projective code family that is universally optimal and that is constructed using ovoids in projective space. See [3; pg. 107][4; pg. 192] for further details.Cousin
- Universally optimal \(q\)-ary code— Several shortened and punctured versions of the ovoid code are LP universally optimal codes [5].
Primary Hierarchy
Parents
The ovoid code is a two-weight projective code [6,7][8; Table 7.1].
The ovoid code is a \(q\)-ary sharp configuration [9; Table 12.1].
Ovoid code
References
- [1]
- R. C. Bose (1947). Mathematical theory of the symmetrical factorial design. Sankhyā: The Indian Journal of Statistics, 107-166.
- [2]
- B. Qvist. Some remarks concerning curves of the second degree in a finite plane. Suomalainen tiedeakatemia, 1952.
- [3]
- R. Calderbank and W. M. Kantor, “The Geometry of Two-Weight Codes”, Bulletin of the London Mathematical Society 18, 97 (1986) DOI
- [4]
- J. Bierbrauer, Introduction to Coding Theory (Chapman and Hall/CRC, 2016) DOI
- [5]
- H. Cohn and Y. Zhao, “Energy-Minimizing Error-Correcting Codes”, IEEE Transactions on Information Theory 60, 7442 (2014) arXiv:1212.1913 DOI
- [6]
- N. Tzanakis and J. Wolfskill, “The diophantine equation x2 = 4qa2 + 4q + 1, with an application to coding theory”, Journal of Number Theory 26, 96 (1987) DOI
- [7]
- A. E. Brouwer and H. Van Maldeghem, Strongly Regular Graphs (Cambridge University Press, 2022) DOI
- [8]
- R. A. Games, “The packing problem for projective geometries over GF(3) with dimension greater than five”, Journal of Combinatorial Theory, Series A 35, 126 (1983) DOI
- [9]
- P. Boyvalenkov, D. Danev, "Linear programming bounds." 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:
“Ovoid code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/bose_qvist