Geodesic
Minimum weight bases for quaternary Reed -- Muller codes
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1358-1366

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The quaternary Plotkin and BQ-Plotkin constructions giving the families of quaternary Reed – Muller codes were presented in 2009. The Gray map image of the obtained $\mathbb{Z}_4$-linear codes have the same parameters and fundamental properties as the codes in the classical binary linear Reed – Muller family. We have found one more general property for the families of quaternary Reed – Muller codes that is common with binary Reed – Muller codes: all these quaternary codes have bases of minimum weight codewords. The bases are constructed by induction.
Keywords: Reed – Muller code, quaternary code, additive code, quaternary Reed – Muller code, minimum weight basis, $\mathbb{Z}_4$-linear code. 
@article{SEMR_2021_18_2_a40,
     author = {F. I. Solov'eva},
     title = {Minimum weight bases for quaternary {Reed} -- {Muller} codes},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1358--1366},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a40/}
}
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F. I. Solov'eva. Minimum weight bases for quaternary Reed -- Muller codes. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1358-1366. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a40/