Ovoid code[1,2] 

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.

Parents

Cousin

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]
P. Boyvalenkov, D. Danev, "Linear programming bounds." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
[6]
H. Cohn and Y. Zhao, “Energy-Minimizing Error-Correcting Codes”, IEEE Transactions on Information Theory 60, 7442 (2014) arXiv:1212.1913 DOI
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Zoo Code ID: bose_qvist

Cite as:
“Ovoid code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/bose_qvist
BibTeX:
@incollection{eczoo_bose_qvist, title={Ovoid code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/bose_qvist} }
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Permanent link:
https://errorcorrectionzoo.org/c/bose_qvist

Cite as:

“Ovoid code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/bose_qvist

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