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Hirschfeld code[1]

Description

A projective geometry code that is an example of an MDS code that is not an RS code; see [2; Exam. 7.6] for the description.

Member of code lists

Primary Hierarchy

Classical Domain
Galois-field Kingdom
\(q\)-ary codeECC
Additive \(q\)-ary codeECC
Linear \(q\)-ary codeECC
Projective geometry code
Parents
Projective geometry code
Maximum distance separable (MDS) codeLinear \(q\)-ary OA LRC Distributed-storage \(t\)-design Universally optimal ECC
The Hirschfeld code is a rare example of an MDS code that is not related to an RS code.
Hirschfeld code

References

[1]
J. W. P. Hirschfeld. Rational curves on quadrics over finite fields of characteristic two. Rend. Mat. (6), 4:773–795, 1971.
[2]
S. Ball, Finite Geometry and Combinatorial Applications (Cambridge University Press, 2015) DOI
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Zoo Code ID: hirschfeld

Cite as:
“Hirschfeld code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/hirschfeld
BibTeX:
@incollection{eczoo_hirschfeld, title={Hirschfeld code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/hirschfeld} }
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Permanent link:
https://errorcorrectionzoo.org/c/hirschfeld

Cite as:

“Hirschfeld code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/hirschfeld

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/easy/hirschfeld.yml.