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Flag-variety code[1]

Description

Evaluation code of polynomials evaluated on points lying on a flag variety.

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
Parents
Polynomial evaluation code
Flag-variety codes are polynomial evaluation codes with \(\cal X\) being a flag variety.
Flag-variety code
Children
Grassmannian code
Grassmannian codes are flag-variety evaluation codes with the flag variety being a Grassmannian.
Hermitian-hypersurface code
Hermitian-hypersurface codes are flag-variety evaluation codes with the flag variety being a Hermitian hypersurface.
Quadric code
Quadric codes are flag-variety evaluation codes with the flag variety being a quadric hypersurface.
Schubert code
Schubert codes are flag-variety evaluation codes with the flag variety being a Schubert variety.

References

[1]
F. Rodier, “Codes from flag varieties over a finite field”, Journal of Pure and Applied Algebra 178, 203 (2003) DOI
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Zoo Code ID: flag_variety

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

Cite as:

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

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