Hermitian-hypersurface code[1]

Description

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

Parent

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

Cousin

  • Hermitian code — Hermitian-hypersurface codes reduce to Hermitian codes of polynomials when the hypersurface is a curve.

References

[1]
I. M. Chakravarti, “Families of Codes with Few Distinct Weights from Singular and Non-Singular Hermitian Varieties and Quadrics in Projective Geometries and Hadamard Difference Sets and Designs Associated with Two-Weight Codes”, Coding Theory and Design Theory 35 (1990) DOI
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Zoo Code ID: hermitian_hypersurface

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

Cite as:

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

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