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Quadric code[1,2]

Description

Evaluation code of polynomials evaluated on points lying on a quadric hypersurface.

Member of code lists

Primary Hierarchy

Classical Domain
Galois-field Kingdom
\(q\)-ary codeECC
Additive \(q\)-ary codeECC
Linear \(q\)-ary codeECC
Evaluation code
Polynomial evaluation code
Flag-variety code
Parents
Flag-variety code
Quadric codes are flag-variety evaluation codes with the flag variety being a quadric hypersurface.
Quadric code

References

[1]
J. Wolfmann, “Codes projectifs a deux ou trois poids associfs aux hyperquadriques d’une geometrie finie”, Discrete Mathematics 13, 185 (1975) DOI
[2]
Y. Aubry, “Reed-Muller codes associated to projective algebraic varieties”, Lecture Notes in Mathematics 4 (1992) DOI
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Zoo Code ID: quadric

Cite as:
“Quadric code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quadric
BibTeX:
@incollection{eczoo_quadric, title={Quadric code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/quadric} }
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Permanent link:
https://errorcorrectionzoo.org/c/quadric

Cite as:

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/ag/varieties/quadric.yml.