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Sloane-Whitehead code[1]

Description

Member of an infinite \((n,\lambda\cdot 2^{n-m-1},3)\) nonlinear code family for any \(n\) satisfying \(2^m \leq n < 3\cdot 2^{m-1}\) for some \(m\) and for \(\lambda\in\{20/16,19/16,18/16\}\). Such a code has more codewords than any linear code with the same length and distance. The code is constructed by applying the \((u|u+v)\) construction recursively to the Julin-Golay codes [1][2; Secs. 2.7 and 2.9].

Member of code lists

Primary Hierarchy

Classical Domain
Binary Kingdom
Binary codeECC
Parents
Binary code
\((u|u+v)\)-construction codeECC
Small-distance block codeECC
Sloane-Whitehead code
Children
Julin-Golay code
Julin-Golay codes are the starting codes for the Sloane-Whitehead construction [1][2; Secs. 2.7 and 2.9].

References

[1]
N. Sloane and D. Whitehead, “New family of single-error correcting codes”, IEEE Transactions on Information Theory 16, 717 (1970) DOI
[2]
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes (Elsevier, 1977)
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Zoo Code ID: sloane_whitehead

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

Cite as:

“Sloane-Whitehead code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/sloane_whitehead

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/bits/nonlinear/sphere_packing/sloane_whitehead.yml.