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Quaternary RM (QRM) code[1]

Description

A quaternary linear code over \(\mathbb{Z}_4\) whose mod-two reduction is an RM code. This code subsumes the quaternary images of the Kerdock and Preparata codes under the Gray map . The code is usually noted as QRM\((r,m)\), with its mod-two reduction yielding the RM code RM\((r,m)\) [1; Thm. 19].

Cousins

References

[1]
A. R. Hammons Jr., P. V. Kumar, A. R. Calderbank, N. J. A. Sloane, and P. Solé, “The Z_4-Linearity of Kerdock, Preparata, Goethals and Related Codes”, (2002) arXiv:math/0207208
[2]
A. A. NECHAEV, “Kerdock code in a cyclic form”, Discrete Mathematics and Applications 1, (1991) DOI
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Zoo Code ID: quaternary_reed_muller

Cite as:
“Quaternary RM (QRM) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/quaternary_reed_muller
BibTeX:
@incollection{eczoo_quaternary_reed_muller, title={Quaternary RM (QRM) code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/quaternary_reed_muller} }
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Permanent link:
https://errorcorrectionzoo.org/c/quaternary_reed_muller

Cite as:

“Quaternary RM (QRM) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/quaternary_reed_muller

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/rings/over_zq/over_z4/linear_over_z4/rm/quaternary_reed_muller.yml.