Recently, new families of quaternary linear Reed-Muller codes have been introduced. They satisfy that, after the Gray map, the corresponding ℤ4-linear codes have the same parameters and properties as the codes of the binary linear Reed-Muller family. A structural invariant, the dimension of the kernel, for binary codes is used to classify completely these ℤ4-linear codes. The dimension of the kernel for these ℤ4-linear codes is established generalizing the known results about the dimension of the kernel for ℤ4-linear Hadamard and ℤ4-linear extended 1-perfect codes. © 2011 IEEE.
- ℤ -linear codes 4
- quaternary codes
- Reed-Muller codes
Pernas, J., Pujol, J., & Villanueva, M. (2011). Classification of some families of quaternary Reed-Muller codes. IEEE Transactions on Information Theory, 57(9), 6043-6051. . https://doi.org/10.1109/TIT.2011.2119465