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All binary linear codes of lengths up to 18 or redundancy up to 10 are normal - MaRDI portal

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All binary linear codes of lengths up to 18 or redundancy up to 10 are normal (Q660087)

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scientific article; zbMATH DE number 6000193
Language Label Description Also known as
English
All binary linear codes of lengths up to 18 or redundancy up to 10 are normal
scientific article; zbMATH DE number 6000193

    Statements

    All binary linear codes of lengths up to 18 or redundancy up to 10 are normal (English)
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    25 January 2012
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    For a survey of covering codes, see for example [\textit{G. Cohen}, \textit{I. Honkala}, \textit{S. Litsyn} and \textit{A. Lobstein}, Covering codes. Amsterdam: Elsevier (1997; Zbl 0874.94001)]. Normality and amalgamated direct sum are used to construct good covering codes, i.e., codes with small covering radius compared to others of the same length and dimension. This kind of approach requires the constituent codes to be normal. Hence, much research has been focused on the question: which codes are normal? The author proves in this paper the normality of the binary linear codes of lengths 16, 17 and 18, or redundancy 10.
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    binary linear codes
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    normal codes
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    covering radius
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    least covering radius
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