Abstract
Recently, new families of quaternary linear Reed-Muller codes such that, after the Gray map, the corresponding ℤ4-linear codes have the same parameters and properties as the codes in the usual binary linear Reed-Muller family have been introduced. A structural invariant, the kernel dimension, for binary codes can be used to classify these ℤ4-linear codes. The kernel dimension for these ℤ4-linear codes is established generalizing the known results about the kernel dimension for ℤ4-linear Hadamard and ℤ4-linear extended 1-perfect codes.
Keywords
This work was supported in part by the Spanish MEC and the European FEDER under Grant MTM2006-03250.
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Pernas, J., Pujol, J., Villanueva, M. (2008). Kernel Dimension for Some Families of Quaternary Reed-Muller Codes. In: Calmet, J., Geiselmann, W., Müller-Quade, J. (eds) Mathematical Methods in Computer Science. Lecture Notes in Computer Science, vol 5393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89994-5_11
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DOI: https://doi.org/10.1007/978-3-540-89994-5_11
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