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\([78,6,56]_4\) Hill-cap code[1]

Description

Projective two-weight quaternary code based on a cap that corresponds to a strongly regular graph [2; Table 7.1].

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
Projective two-weight codeLinear \(q\)-ary ECC
Hill projective-cap code
Parents
Hill projective-cap code
\(q\)-ary sharp configurationOA Sharp configuration Universally optimal ECC \(t\)-design
The \([78,6,56]_4\) Hill-cap code is a \(q\)-ary sharp configuration [3; Table 12.1].
\([78,6,56]_4\) Hill-cap code

References

[1]
R. Hill, Caps and groups, pp. 389–394 in: Proc. Rome 1973, Atti dei Convegni Lincei, 1976
[2]
R. A. Games, “The packing problem for projective geometries over GF(3) with dimension greater than five”, Journal of Combinatorial Theory, Series A 35, 126 (1983) DOI
[3]
P. Boyvalenkov, D. Danev, “Linear programming bounds”, Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021), pp. 251-266 DOI
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Zoo Code ID: hill_78_6_56

Cite as:
“\([78,6,56]_4\) Hill-cap code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/hill_78_6_56, arXiv:2606.11484
BibTeX:
@incollection{eczoo_hill_78_6_56,
title={\([78,6,56]_4\) Hill-cap 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/hill_78_6_56}
}
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Permanent link:
https://errorcorrectionzoo.org/c/hill_78_6_56

Cite as:

“\([78,6,56]_4\) Hill-cap code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/hill_78_6_56, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/projective/projective_two_weight/hill_cap/hill_78_6_56.yml.