Quaternary RM (QRM) code[1]
Description
A quaternary linear code over \(\mathbb{Z}_4\) that is a quaternary version of the RM code in that its binary image under the Gray map 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 image under the Gray map yielding the RM code RM\((r,m)\) [1; Thm. 19].
Parent
Cousins
- Reed-Muller (RM) code — The image of the QRM\((r,m)\) code under the Gray map is the RM\((r,m)\) code [1; Thm. 19].
- Gray code — The image of the QRM\((r,m)\) code under the Gray map is the RM\((r,m)\) code [1; Thm. 19].
- Preparata code — The image of the Preparata code under the Gray map yields the QRM\((m-2,m)\) code [1; Thm. 19].
- Kerdock code — The image of the Kerdock code under the Gray map yields the QRM\((1,m)\) code [1; Thm. 19].
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
Page edit log
- Victor V. Albert (2024-08-15) — most recent
Cite as:
“Quaternary RM (QRM) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/quaternary_reed_muller