Extended Hamming code[13] 

Description

Member of an infinite family of binary linear codes with parameters \([2^r,2^r-r-1, 4]\) for \(r \geq 2\) that are extensions of the Hamming codes by a parity-check bit.

Parents

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Cousins

References

[1]
C. E. Shannon, “A Mathematical Theory of Communication”, Bell System Technical Journal 27, 379 (1948) DOI
[2]
R. W. Hamming, “Error Detecting and Error Correcting Codes”, Bell System Technical Journal 29, 147 (1950) DOI
[3]
M. J. E. Golay, Notes on digital coding, Proc. IEEE, 37 (1949) 657.
[4]
H. Cohn and Y. Zhao, “Energy-Minimizing Error-Correcting Codes”, IEEE Transactions on Information Theory 60, 7442 (2014) arXiv:1212.1913 DOI
[5]
J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups (Springer New York, 1999) DOI
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Zoo Code ID: extended_hamming

Cite as:
“Extended Hamming code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/extended_hamming
BibTeX:
@incollection{eczoo_extended_hamming, title={Extended Hamming code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/extended_hamming} }
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Permanent link:
https://errorcorrectionzoo.org/c/extended_hamming

Cite as:

“Extended Hamming code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/extended_hamming

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/bits/easy/hamming/extended_hamming.yml.