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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Construction of Additive Reed-Muller Codes
verfasst von : Jaume Pujol, J. Rifà, L. Ronquillo
Erschienen in: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Verlag: Springer Berlin Heidelberg
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The well known Plotkin construction is, in the current paper, generalized and used to yield new families of ℤ
2
ℤ
4
-additive codes, whose length, dimension as well as minimum distance are studied. These new constructions enable us to obtain families of ℤ
2
ℤ
4
-additive codes such that, under the Gray map, the corresponding binary codes have the same parameters and properties as the usual binary linear Reed-Muller codes. Moreover, the first family is the usual binary linear Reed-Muller family.