Glynn code[1] 


The unique trace-Hermitian self-dual \([10,5,6]_9\) code, constructed using a 10-arc in \(PG(4,9)\) that is not a rational curve.

The Glynn code is the unique trace-Hermitian code for its parameters, and is not Euclidean self-dual [24].




D. G. Glynn, “The non-classical 10-arc of PG(4, 9)”, Discrete Mathematics 59, 43 (1986) DOI
T. Baicheva, I. Bouyukliev, S. Dodunekov, and W. Willems, “On the [10; 5; 6] Reed-Solomon and Glynn codes,” Mathematica Balkanica, New Series, vol. 18, pp. 67–78, 200
T. A. Gulliver, J.-L. Kim, and Y. Lee, “New MDS or Near-MDS Self-Dual Codes”, IEEE Transactions on Information Theory 54, 4354 (2008) DOI
M. Grassl and T. A. Gulliver, “On circulant self-dual codes over small fields”, Designs, Codes and Cryptography 52, 57 (2009) DOI
M. Grassl and M. Rotteler, “Quantum MDS codes over small fields”, 2015 IEEE International Symposium on Information Theory (ISIT) (2015) arXiv:1502.05267 DOI
S. Ball, “Some constructions of quantum MDS codes”, (2021) arXiv:1907.04391
S. Ball and R. Vilar, “The geometry of Hermitian self-orthogonal codes”, (2021) arXiv:2108.08088
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Zoo Code ID: glynn

Cite as:
“Glynn code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.
@incollection{eczoo_glynn, title={Glynn code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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“Glynn code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.