Abstract
New quaternary Plotkin constructions are given and are used to obtain new families of quaternary codes. The parameters of the obtained codes, such as the length, the dimension and the minimum distance are studied. Using these constructions new families of quaternary Reed-Muller codes are built with the peculiarity that after using the Gray map the obtained ℤ4-linear codes have the same parameters as the codes in the classical binary linear Reed-Muller family.
This work has been partially supported by the Spanish MEC and the European FEDER Grant MTM2006-03250 and also by the UAB grant PNL2006-13.
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Pujol, J., Rifà, J., Solov’eva, F.I. (2007). Quaternary Plotkin Constructions and Quaternary Reed-Muller Codes. In: Boztaş, S., Lu, HF.(. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2007. Lecture Notes in Computer Science, vol 4851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77224-8_19
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DOI: https://doi.org/10.1007/978-3-540-77224-8_19
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