\([56,6,36]_3\) Hill-cap code[1] 

Description

Projective two-weight ternary code based on the Games graph [3][2; Table 19.1] and Hill's 56-cap [1]. Its automorphism group contains \(PSL_3(4)\) [4].

Parents

References

[1]
Hill, R. (1973). On the largest size of cap in s53. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, 54(3), 378-384.
[2]
A. E. Brouwer, "Two-weight Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
[3]
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
[4]
N. Pace and A. Sonnino, “On linear codes admitting large automorphism groups”, Designs, Codes and Cryptography 83, 115 (2016) DOI
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Zoo Code ID: hill_56_6_36

Cite as:
“\([56,6,36]_3\) Hill-cap code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/hill_56_6_36
BibTeX:
@incollection{eczoo_hill_56_6_36, title={\([56,6,36]_3\) Hill-cap code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/hill_56_6_36} }
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https://errorcorrectionzoo.org/c/hill_56_6_36

Cite as:

“\([56,6,36]_3\) Hill-cap code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/hill_56_6_36

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/projective/projective_two_weight/hill_cap/hill_56_6_36.yml.