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Hill projective-cap code[1]

Description

Member of a projective code family that contains of \(q\)-ary sharp configurations and that is constructed using projective caps.

Cousin

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
Parents
Projective two-weight code
Hill projective-cap codes are projective two-weight codes on projective caps [3; Table 19.1].
Hill projective-cap code
Children
\([56,6,36]_3\) Hill-cap code
\([78,6,56]_4\) Hill-cap code

References

[1]
Hill, R. (1973). Caps and groups. Colloquio Internazionale sulle Teorie Combinatorie (Rome, 1973), 2, 389-394.
[2]
P. Boyvalenkov, D. Danev, "Linear programming bounds." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
[3]
A. E. Brouwer, "Two-weight Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
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Zoo Code ID: hill_cap

Cite as:
“Hill projective-cap code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/hill_cap
BibTeX:
@incollection{eczoo_hill_cap, title={Hill projective-cap code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/hill_cap} }
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Permanent link:
https://errorcorrectionzoo.org/c/hill_cap

Cite as:

“Hill projective-cap code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/hill_cap

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