[Jump to code hierarchy]

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 code
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
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)— see instructions

edit on this site

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} }
Share via:
Twitter | Mastodon |  | E-mail
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/edit/main/codes/classical/q-ary_digits/ag/varieties/hermitian_hypersurface.yml.