Geodesic
Linear and additive perfect codes over skew fields and quasi skew fields
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1093-1107

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In this paper, we propose a general construction of linear perfect codes over infinite skew fields and quasi skew fields with right (left) unity. A complete classification of such codes over associative skew fields is given. Since the cardinality of the considered skew fields is infinite, the constructed codes have an infinite length. In the previous work, we considered codes over infinite countable fields, the length of which was also countable. We now remove this restriction and assume that the cardinality of the skew field and the length of the codes can be arbitrary (not necessarily countable).
Keywords: skew field, quasi skew field, perfect code, checking matrix, octonions.
Mots-clés : quaternions 
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     author = {S. A. Malyugin},
     title = {Linear and additive perfect codes over skew fields and quasi skew fields},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1093--1107},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a37/}
}
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S. A. Malyugin. Linear and additive perfect codes over skew fields and quasi skew fields. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1093-1107. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a37/