Flag-variety code[1] 

Description

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

Parent

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/tree/main/codes/classical/q-ary_digits/ag/varieties/flag_variety.yml.