Construction of Additive Reed-Muller Codes
J. Pujol, J. Rif\`a, L. Ronquillo
TL;DR
This paper generalizes the Plotkin construction to create new families of Z2Z4-additive codes, which under the Gray map resemble classical binary Reed-Muller codes in parameters and properties.
Contribution
The paper introduces a generalized construction method for Z2Z4-additive codes that replicate the properties of Reed-Muller codes under the Gray map.
Findings
New families of Z2Z4-additive codes constructed
Codes under Gray map have parameters matching Reed-Muller codes
First family coincides with classical binary Reed-Muller codes
Abstract
The well known Plotkin construction is, in the current paper, generalized and used to yield new families of Z2Z4-additive codes, whose length, dimension as well as minimum distance are studied. These new constructions enable us to obtain families of Z2Z4-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.
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Taxonomy
TopicsCoding theory and cryptography