[Jump to code hierarchy]

Flag-variety code[1]

Description

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

Cousin

Member of code lists

Primary Hierarchy

Classical Domain
Galois-field Kingdom
\(q\)-ary codeECC
Additive \(q\)-ary codeECC
Linear \(q\)-ary codeECC
Evaluation codeAG ECC
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 evaluation code
Grassmannian evaluation 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 evaluation code
Schubert evaluation 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
[2]
V. Lakshmibai and J. Brown, The Grassmannian Variety (Springer New York, 2015) DOI
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)

— see instructions

Zoo Code ID: flag_variety

Cite as:
“Flag-variety code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/flag_variety, arXiv:2606.11484
BibTeX:
@incollection{eczoo_flag_variety,
title={Flag-variety code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/flag_variety}
}
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/flag_variety

Cite as:

“Flag-variety code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/flag_variety, arXiv:2606.11484

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