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Hermitian-hypersurface code[1]

Description

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

Cousin

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

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

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”, The IMA Volumes in Mathematics and Its Applications 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.), 2026. https://errorcorrectionzoo.org/c/hermitian_hypersurface, arXiv:2606.11484
BibTeX:
@incollection{eczoo_hermitian_hypersurface,
title={Hermitian-hypersurface 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/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.), 2026. https://errorcorrectionzoo.org/c/hermitian_hypersurface, arXiv:2606.11484

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