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Hirschfeld code[1]

Description

A \([q+1,4,q-2]_q\) projective geometry code for non-prime \(q\) that is an example of an MDS code that is not an RS code; see [2; Exam. 7.6] for the generator matrix.

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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) codeLRC Distributed-storage Linear \(q\)-ary OA Universally optimal ECC \(t\)-design
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.), 2026. https://errorcorrectionzoo.org/c/hirschfeld, arXiv:2606.11484
BibTeX:
@incollection{eczoo_hirschfeld,
title={Hirschfeld 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/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.), 2026. https://errorcorrectionzoo.org/c/hirschfeld, arXiv:2606.11484

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