Classification of Some Families of Quaternary Reed-Muller Codes
Recently, new families of quaternary linear Reed-Muller codes have been introduced. They satisfy that, after the Gray map, the corresponding Z(4)-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 Z(4)-linear codes. The dimension of the kernel for these Z(4)-linear codes is established generalizing the known results about the dimension of the kernel for Z(4)-linear Hadamard and Z(4)-linear extended 1-perfect codes.
reed-muller codes z(4)-linear codes kernel quaternary codes