Schubert code[1,2] 

Description

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

Protection

Minimum distance bounds computed in Refs. [24].

Parent

  • Flag-variety code — Schubert codes are flag-variety evaluation codes with the flag variety being a Schubert variety.

Cousin

  • Grassmannian code — Schubert varieties are subvarieties of Grassmannians, and Schubert codes were initially constructed as a generalization of Grassmannian codes.

References

[1]
S. R. Ghorpade and G. Lachaud, “Higher Weights of Grassmann Codes”, Coding Theory, Cryptography and Related Areas 122 (2000) DOI
[2]
Hao Chen, “On the minimum distances of Schubert codes”, IEEE Transactions on Information Theory 46, 1535 (2000) DOI
[3]
L. Guerra and R. Vincenti, “On the Linear Codes Arising from Schubert Varieties”, Designs, Codes and Cryptography 33, 173 (2004) DOI
[4]
S. R. Ghorpade and M. A. Tsfasman, “Schubert varieties, linear codes and enumerative combinatorics”, Finite Fields and Their Applications 11, 684 (2005) DOI
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Zoo Code ID: schubert

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

Cite as:

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

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